You may well have a doozy of a question there. Everybody thinks they know the song, but maybe what you quotes is all there is. All I know of are parodies. Here are a couple:

Here comes the bride,
all dressed in white.
Stepped on a turtle,
and down came her girdle.


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Here comes the bride
all dressed in white
slipped on a banana peel
and went for a ride.


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Here comes the bride, all dressed in white
I said I do, to marry you
You said you'd carry a slob like me
You said you'd carry a slob like me
Bride in black
Bride In Black
by Rackets And Drapes


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