"Bully of the Town" doesn't seem to be the same song as "Bully in the Alley", which as I understand it is a rowing chantey. DT has both, but here are some more verses to "Bully in the Alley":

Cho: So help me, Bob, I'm bully in the alley,
    Way, hey, bully in the alley,
    Help me, Bob, I'm bully in the alley,
    Bully down in Shinbone Al.
   
    Sally is the girl that I love dearly,
    Way, hey, bully in the alley;
    Sally is the girl that I splice nearly,
    Bully down in Shinbone Al.

    For seven long years I courted Sally,
    All she did was dilly-dally.

    I bought her silks, I bought her laces,
    Took her out to all of the places.

    So I'll leave Sal and I'll be a sailor,
    I'll leave Sal and ship aboard a whaler.

    When I get home, I'll marry Sally,
    We'll have kids and count 'em by the tally.

    I shipped on board of the Robert E. Lee, boys;
    Made a lot of money, spent it fast and free, boys.

    Got British ammunition and French champagne;
    When I get to Charleston, gonna feel no pain.

    I shipped on board of a Charleston liner;
    Carolina's fine, but St. George is finer.