A lot of new and old jazz is built on R, 3, 5, 3. That means (Root of the scale, 3rd note, 5th note, 3rd note) or R, 5, 3, 5.

Major Scale
G--------------2-4-5-----------------
D--------{2}-3-[5]-------------------
A-<3>-5------------------------------
E------------------------------------

{3rd}
[5th]

G-------------------------------------
D-------------------------------------
A-----{2}-[5]-{2}---------------------
E-<3>---------------------------------


r,3,5,3 bass line
G-------------------------------6-9-6---4-7-4-------------------
D-------------4-7-4----6-9-6--7--------5-------4-7-4---2-5-2----
A----4-7-4--5---------7-----------------------5------3----------
E--5------------------------------------------------------------

Repeat as necessary.
r,5,3,5 bass line
G----------------------------9-6-9---7-4-7-----------------------
D------------7-4-7---9-6-9-7-------5---------7-4-7---2-5-2-------
A----7-4-7-5-------7-----------------------5-------3-------------
E--5-------------------------------------------------------------

Throw in a jazzy intro
A--77-5-------
E-------8-7---

or

D-----7-5-------
A--55-----8-----