Evidence from Carpenter's singers indicates a fair antiquity for "Bully in the Alley":

James Forman was born 1844 and went to sea in 1856, and Carpenter's notes say 'Learned as a boy before going to sea.'

Edward Robinson, was older (b 1834, to sea 1846), and Carpenter's handwritten notes to his version say 'cotton screwing' and (puzzlingly) 'Captain Page heard the chantey about 1853.'

Captain Page (b 1835, to sea 1849) was another old salt, apparently at the same sailors' rest home as Capt Robinson.

These are just snippets available from the online index: when Carpenter's full text and notes are available, we may well be able to push the dates of several shanties back from the '80s to the '50s or even '40s.