G'day,Charley Noble: "... a true "bully" in the alley ..."
The discussions above seem to miss the meaning that I take, from common British useage, where "bully" (initially as an adjective, but that can be used as a noun, omitting the subject) means "very good", or "first rate".
He is saying that he is top dog in Shinbone Alley ... ? It certainly sounds more like a boastful sailor's view of life on shore leave.
Regards,
Bob Bolton