I've also tabbed Caravan and BU2B and I must say this is one of the hardest 
basslines I've ever learned! 
Great one though, lots of attitude from Geddy here. Listen for the timing as it is tricky! Enjoy!

This is a very long tab I admit, but Geddy barely if ever plays the same part twice in this song. 
I tried to be as accurate as possible to what I heard in the song.

Rush - Headlong Flight

Intro
G|---------------------------------12h14p12-----|
D|-12h14p12--------12h14p12-----------------14--|
A|----------14~-14----------14~-14--------------|
E|----------------------------------------------|

G|------------------------------------------------|
D|-12h14p12--------12h14p12----12-----------------|
A|----------14~-14----------14----14-12h14p12-----|
E|--------------------------------------------15--| x7

G|-------|
D|-------|
A|-------|
E|-12\---| (slide out to nothing)


Intro Part 2 (Bastille Day-esque riff)
G|------------------------------------|
D|------------------------------------|
A|------------------------------------|
E|---------0-0-0-0-----------------0--|

G|---------9-7---7----------------|
D|-------------9-----7-5---5------|
A|-----------------------7---7-7--|
E|--------------------------------| (You can use pull-offs but sounds like 

Geddy is hitting every note)


Verse 1 Part 1
G|----------------------------------|
D|----------------------------------|
A|-------------------5-5-5-5-3-3-3--|
E|-0-0-0h3p0-0h5p0-0----------------|

G|-----------------------------------|
D|-----------------------------------|
A|-------------------5h7-7-7-7-7-5\--|
E|-0-0-0h3p0-0h5p0-0-----------------|

G|----------------------------------|
D|----------------------------------|
A|-------------------5-5-5-5-3-3-3--|
E|-0-0-0h3p0-0h5p0-0----------------|

G|-----------------------------------|
D|-----------------------------------|
A|-------------------5h7-7-7-5-7-7\--|
E|-0---0h3p0-0h5p0-0-----------------|

G|----------------------------------|
D|----------------------------------|
A|-------------------5-5-5-5-3-3-3--|
E|-0-0-0h3p0-0h5p0-0----------------|

G|-----------------------------------|
D|-------------------------------5\--|
A|-------------------5h7-7-7-7-7-----|
E|-0---0h3p0-0h5p0-0-----------------|

G|----------------------------------|
D|----------------------------------|
A|-------------------5-5-5-5-3-3-3--|
E|-0-0-0h3p0-0h5p0-0----------------|

G|-----------------------------------|
D|-----------------------------------|
A|-------------------5h7-7-7-5-7-5\--|
E|-0---0h3p0-0h5p0-0-----------------|


Verse 1 Part 2
G|-------------3-5---0-3-0-2-0------|
D|-------2---4-----------------3-2--|
A|-3---3----------------------------|
E|----------------------------------|

G|---------------5-3-2-0------------|
D|-------2---3-5---------3-2-0------|
A|-3---3-----------------------3-2--|
E|----------------------------------|

G|----------------------------|
D|----------------------------|
A|----------------------------|
E|-0---0-3--0-5--0-3--0-3--3--|

G|-------------------------------|
D|-------------------------------|
A|-------------------------------|
E|-0---0-3--0-5--0-3--0-3p0-3p0--|

G|------------------5-4---7-5-4---4h5p4---5-4--------------------|
D|------------5-7-------7-------7-------7-----7-5-4-5-4---4------|
A|------4---7-------------------------------------------7---7----|
E|-5----------------------------------------------------------5--|

G|----------------------------|
D|----------------------------|
A|----------------------------|
E|-0---0-3--0-5--0-3--0-3--3--|

G|-------------------------|
D|-------------------------|
A|-------------------------|
E|-0---0-3--0-5--0-3--0-3--|

G|----------------|
D|----------------|
A|----------------|
E|-0----0----0-0-0|


Verse 2 Part 1
G|-----------------------------------|
D|-----------------------------------|
A|--(2 measures of drum and guitar)--|
E|-----------------------------------|

G|----------------------------------|
D|----------------------------------|
A|-------------------5-5-5-5-3-3-3--|
E|-0-0-0h3p0-0h5p0-0----------------|

G|-----------------------------------|
D|-----------------------------------|
A|-------------------5h7-7-7-7-7-5\--|
E|-0-0-0h3p0-0h5p0-0-----------------|

G|----------------------------------|
D|----------------------------------|
A|-------------------5-5-5-5-3-3-3--|
E|-0-0-0h3p0-0h5p0-0----------------|

G|----------------------------------|
D|---------------7-5-4-5-4---4------|
A|-------------------------7---7-5--|
E|-0---0h3p0-0h5--------------------|


Verse 2 Part 2
G|-------------3-5-----3-0-2-0------|
D|-------2---4-------5---------3-0--|
A|-3---3----------------------------|
E|----------------------------------|

G|---------------5-3-2-3-2-0-5-0-2--|
D|-------2---3-5--------------------|
A|-3---3----------------------------|
E|----------------------------------|

G|-----------------5-4---7-5-4---5-7/8\7-5-8-7-5---5---5---------------|
D|------------5-7------7-------7-----------------7---7---7-5-----------|
A|------4---7------------------------------------------------7-5-------|
E|-5-------------------------------------------------------------8\-5--|

G|-----------------------|
D|-----------------------|
A|-----------------------|
E|-0-----0------0--0--0--|


Chorus

G|-----------------------------------|
D|-----------------------------------|
A|--(8 measures of drum and guitar)--|
E|-----------------------------------|

G|---------------------------------------------------------2h4-2-0----|
D|-------------------------------------------0-2-0-----------------4--|
A|---------------0-2-2-2-2-2-0-2-0-3-3-3-3-3-------0-0-0-0------------|
E|-0-0-0-0-0-0-0------------------------------------------------------|

G|------------------------------------------------------------------|
D|-----2-------2-----------------------------0-2-0------------------|
A|---2-----------0-2-2-2-0-2-0-2-0-3-3-3---3------------------------|
E|-0-----0---0---------------------------3---------4-4-4-4-6-6-6-6--|


Verse 3 Part 1
G|--------------------------|
D|--------------------------|
A|--(2 measures of guitar)--|
E|--------------------------|

G|----------------------------------|
D|----------------------------------|
A|-------------------5-5-5-5-3-3-3--|
E|-0-0-0h3p0-0h5p0-0----------------|

G|--------------------------------------|
D|--------------------------------------|
A|-------------------5h7-7-7-5h7-7-5h7--|
E|-0-0-0h3p0-0h5p0-0--------------------|

G|----------------------------------|
D|----------------------------------|
A|-------------------5-5-5-5-3-3-3--|
E|-0-0-0h3p0-0h5p0-0----------------|

G|------------------------------------|
D|------------------------------------|
A|-------------------5h7-7-7-5-7-5----|
E|-0---0h3p0-0h5p0-0---------------7--|

G|----------------------------------|
D|----------------------------------|
A|-------------------5-5-5-5-3-3-3--|
E|-0-0-0h3p0-0h5p0-0----------------|

G|-----------------------------------|
D|-------------------------------5\--|
A|-------------------5h7-7-7-5-7-----|
E|-0---0h3p0-0h5p0-0-----------------|

G|----------------------------------|
D|----------------------------------|
A|-------------------5-5-5-5-3-3-3--|
E|-0-0-0h3p0-0h5p0-0----------------|

G|--------------------------------------|
D|-------------------7-5-4-5-4---5-4----|
A|-----------------------------7-----7--|
E|-0---0h3p0-0h5p0-0--------------------|

Verse 3 Part 2
G|-------------3-5---0-3-0-2h3p2-0--|
D|-------2---4----------------------|
A|-3---3----------------------------|
E|----------------------------------|

G|---------------5-3-2-3-2h3p2-0------|
D|-------2---3-5-----------------3-2--|
A|-3---3------------------------------|
E|------------------------------------|

G|----------------------------|
D|----------------------------|
A|----------------------------|
E|-0---0-3--0-5--0-3--0-3--3--|

G|-------------------------------|
D|-------------------------------|
A|-------------------------------|
E|-0---0-3--0-5--0-3--0-3p0-3p0--|

G|------------------5-4---7-5-4---4-5-4---5-4-----------------------|
D|------------5-7-------7-------7-------7-----7-5-4-5-4---4---------|
A|------4---7-------------------------------------------7---7--4----|
E|-5-------------------------------------------------------------5--|

G|----------------------------|
D|----------------------------|
A|----------------------------|
E|-0---0-3--0-5--0-3--0-3--3--|

G|-------------------------|
D|-------------------------|
A|-------------------------|
E|-0---0-3--0-5--0-3--0-3--|

G|------------------------------|
D|------------------------------|
A|------------------------------|
E|-0----0----0-0-0----0----0-0--|


Chorus 2
G|--------------------------------------------------------2---4-2----|
D|-------------------------------------------0-2-0----------------4--|
A|---------------0-2-2-2-2-2-0-2-0-3-3-3---3-------0-0-0-------------|
E|-0-0-0-0-0-0-0-------------------------3---------------------------|

G|------------------------------------------------------------------|
D|-----2-------2---------------------------5/7-5--------------------|
A|---2-----------0-2-2-2-0-2-0-2-0-3-3-3-3-------8-7------------------|
E|-0-----0---0---------------------------------------4-4-4-4-6-6-6-6--|


Jam Part 1
G|-------------------------------------|
D|-------------------------------------|
A|-(Drum and guitar only, 2 measures)--|
E|-------------------------------------|

G|---------------------------------|
D|---------------------------------|
A|-5-7-5-7-5-7-5--------5-7-5------|
E|---------------0----0-------0----| x2

G|-----------------------------|
D|-----------------------------|
A|-5-7-5-7-5--------5-7-5------|
E|-----------0----0-------0----|

G|---------------------------------|
D|---------------------------------|
A|-5-7-5-7-5-7-5--------5-7-5------|
E|---------------0----0-------0----|

G|---------------------------------|
D|---------------------------------|
A|-5-7-5-7-5--------5-7-5----------|
E|-----------0----0-------0---0-0--|


Jam Part 2 (Talking Section)
G|-----------------------------------|
D|-----------------------------------|
A|--(2 measures of drum and guitar)--|
E|-----------------------------------|

G|---------------------------|
D|---------------------------|
A|---------------------------| 
E|-0--0h3p0-0-5--0-3--0-3-3--|

G|---------------------------|
D|---------------------------|
A|---------------------------| (The days were dark)
E|-0--0h3p0-0-5--0-3--0-3-0--|

G|---------------------------|
D|---------------------------|
A|---------------------------| (And the nights were bright)
E|-0--0h3p0-0-5--0-3--0-3-3--|

G|-------------------------------|
D|------------9-7-9--9-7-9-7-9\--|
A|-------------------------------| (Hey man...)
E|-0--0h3p0-0--------------------|

G|---------------------------|
D|---------------------------|
A|---------------------------| (I would NEVER trade tomorrow for today)
E|-0--0h3p0-0-5--0-3--0-3-3--|

G|---------------------------------|
D|----------------5---5----5-------|
A|------------5h7---7---7----7-----|
E|-0--0h3p0-0------------------8\--|
 

Jam Part 3 (Solos)
G|---------------------|
D|---------------------|
A|--(2 bar drum solo)--| (Yeah!!!)
E|---------------------|

G|----------------------------------|
D|----------------------------------|
A|-5-7-5-------5-7-5-------5-7-5----|
E|-------0---0-------0---0-------0--| x4

G|----------------------------------|
D|-------------------------5-7-5----|
A|-5-7-5-------5-7-5-------------7--|
E|-------0---0-------0---0----------|

G|----------------------------------|
D|-------------5-7-5---5------------|
A|-5-7-5-------------7---7-5-7-5----|
E|-------0---0-------------------7--|

G|----------------------------------|   \
D|----------------------------------|    |
A|-5-7-5-------5-7-5-------5-7-5----|    |
E|-------0---0-------0---0-------0--|    |
                                          > x5
G|----------------------------------|    |
D|-------------5-7-5---5------------|    |
A|-5-7-5-------------7---7-5-7-5----|    |
E|-------0---0-------------------7--|   /


Jam Part 4
G|---------------------------------|
D|---------------------------------|
A|-3--3-3-3-3-3-3-3-3-3-3-3---3----|
E|--------------------------3---3--|

G|--------------------------------|
D|------------------------4-4-7\--|
A|-5--5-5-5-5-5-5-5-5-7-7---------|
E|--------------------------------|

G|-----------------------------------------------|
D|-----------------------------------------------|
A|-----------------------------------------------|
E|-0----0-0-0----0----0-0-0-0-0----0----0-0-0-0--|

G|----------------------------------|
D|----------------------------------|
A|----------------------------------|
E|-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0--| x3

G|----------------------------|
D|----------------------------|
A|-----------------------14\--|
E|-0-0-0-0-0-0-0-0-0-0-0------|


Verse 4 Part 1
G|----------------------------------|
D|----------------------------------|
A|-------------------5-5-5-5-3-3-3--|
E|-0-0-0h3p0-0h5p0-0----------------|

G|-------------------------------------|
D|-------------------------------------|
A|-------------------5h7-7-7-7-7-5h7\--|
E|-0-0-0h3p0-0h5p0-0-------------------|

G|----------------------------------|
D|----------------------------------|
A|-------------------5-5-5-5-3-3-3--|
E|-0-0-0h3p0-0h5p0-0----------------|

G|----------------------------------|
D|---------------------7----5-------|
A|----------------------------0-7\--|
E|-0---0h3p0-0h5p0-0-0---0----------|


Verse 4 Part 2
G|-------------3-5---0-3-0-2-3-2-0--|
D|-------2---4----------------------|
A|-3---3----------------------------|
E|----------------------------------|

G|---------------5-3-2-3-2-0--------|
D|-------2---3-5-------------3-2-0--|
A|-3---3----------------------------|
E|----------------------------------|

G|----------------------------|
D|----------------------------|
A|----------------------------|
E|-0---0-3--0-5--0-3--0-3--3--|

G|-------------------------------|
D|-------------------------------|
A|-------------------------------|
E|-0---0-3--0-5--0-3--0-3p0-3p0--|

G|------------------7-5---8-5---7-5-4--------------|
D|------------5-7-------7-----7-------7-5-4--------|
A|------4---7-------------------------------7-5-4--|
E|-5-----------------------------------------------|

G|----------------------------|
D|----------------------------|
A|----------------------------|
E|-0---0-3--0-5--0-3--0-3--3--|

G|-------------------------|
D|-------------------------|
A|-------------------------|
E|-0---0-3--0-5--0-3--0-3--|

G|----------------|
D|----------------|
A|----------------|
E|-0----0----0-0-0|


Chorus3

G|-----------------|
D|-----------------|
A|--(Rest 7 bars)--|
E|-----------------|

G|------------------------------------------------|
D|----------------------------------(-Triplets-)--|
A|--7/14-14-0-12-12-0-10-10-0-9-9-0--7-5---5------|
E|--------------------------------------7---7-5---|

G|----------------------------------------------------------------|
D|-----2-------2---------------------------0-2-0------------------|
A|---2-----------0-2-2-2-0-2-0-2-0-3-3-3-3-------6-6-6-6-8-8-8-8--|
E|-0-----0---0----------------------------------------------------|

G|-------------------------------------------------------4----2----0--------|
D|-------------------------------------------0-2-0---------44---44---4-2-0--|
A|---------------0-2-2-2-2-2-0-2-0-3-3-3---3-------0-0-0--------------------|
E|-0-0-0-0-0-0-0-------------------------3----------------------------------|

G|------------------------------------------------------------------|
D|-----2-------2---------------------------------------------9------|
A|---2-----------0-2-2-2-0-2-0-2-0-3-3-3-3-3-2-0--------------------|
E|-0-----0---0-----------------------------------3-5-5-5-5-7---7-7--|

G|---------------------------------------------------7-5-4----------|
D|-----2-------2---------------------5/7-5-4-5-4-----------7-5-4----|
A|---2-----------0-2-2-2-0-2-0-2-0-3-------------7---------------7--|
E|-0-----0-0-0-------------------------------------0----------------|

G|-------------------|
D|-------------------|
A|-------------------|
E|-0----0-0-0--0000--|



| /  slide up
| \  slide down
| h  hammer-on
| p  pull-off
| ~  vibrato
| +  harmonic
| x  Mute note
==============================================================================