Hmmm. The page that Stewie links to has lyrics for BOTH versions combined. Are they really all part of the same song?
Jerry Silverman's Folk Song Encyclopedia has "the Bully of the Town" and "The New Bully Song," same lyrics as the version we have in the Forum ("Have you heard about the bully"), but two different tunes. The song is also in Best-Loved Songs of the American People, but I don't have that one.
Search for bully at the Library of Congress and you'll find at least a couple of recordings. Great stuff. I'm glad you called it to our attention.
-Joe Offer-