The bridge is the trickiest part of the song. After the third "ring them bells" the bass 
line goes down stepwise from Ab   G   F#  F   E

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True chords for Piano

Bm                                  Em        Bm
Ring them bells ye heathen from the city that dreams
Bm                                             F#m
Ring them bells from the sanctuaries cross the valleys and streams
Em                           Bm
For they're deep and they're wide
Abm7                 Em
And the world on its side
Bm                  Em
And time is running backwards
F#m           Bm
And so is the bride.

Bm                                     Em        Bm
Ring them bells Saint Peter where the four winds blow
Bm                                      F#m
Ring them bells with an ironhand so the people will know
Em                 Bm
For it's rush hour now
Abm7			Em
On the wheel and the plow
Bm                   Em            F#m    Bm
And the sun is going down upon the sacred cow.

Instrumental Solo

(Same progression as above)
Bm   Em   Bm   Bm   F#m   Em   Bm
  Abm7   Em   Bm   Em   F#m   Bm


Bm                                   Em        Bm
Ring them bells Sweet martha for the poor man's son
Bm                                          F#m
Ring them bells so the world will know that God is one
Em                   Bm
Oh the shepherd is asleep
Abm7			Em
Where the willows weep
        Bm            Em          F#m   Bm
And the mountains are filled with lost sheep

Bridge:
             Abm			Bm
Ring them bells for the blind and the deaf
             Abm			Bm
Ring them bells for all of us who are left
             Abm               Gaug[G B Eb]
Ring them bells for the chosen few
                   B                 Abm7/F
Who will judge the many when the game is through
Em                                Bm
Ring them bells for the time that flies
                   Em
For the child that cries
                   F#m
When the innocence dies.


Bm                                       Em        Bm
Ring them bells Saint Catherine from the top of the room
Bm                                  F#m
Ring them from the fortress for the lilies that bloom
Em               Bm           Abm7        Em
Oh the lines are long and the fighting is strong
            Bm                Em               F#m       Bm
And they're breaking down the distance between right and wrong.

Instrumental Solo
(Same progression)
Bm   Em   Bm   Bm   F#m   Em   Bm
  Abm7   Em   Bm   Em   F#m   Bm