The bridge is the trickiest part of the song. After the third "ring them bells" the bass 
line goes down stepwise from G#   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
G#m7                 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
G#m7			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
  G#m7   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
G#m7			Em
Where the willows weep
        Bm            Em          F#m   Bm
And the mountains are filled with lost sheep

Bridge:
             G#m			Bm
Ring them bells for the blind and the deaf
             G#m			Bm
Ring them bells for all of us who are left
             G#m               Gaug[G B D#]
Ring them bells for the chosen few
                   Bm/F#                 G#m7/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           G#m7        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
  G#m7   Em   Bm   Em   F#m   Bm