According to Halliwell's "Dictionary of Archaic Words" (1850) Bully means, and I quote, "A companion, a familiar term of address, as Bully Jack, Bully Bob, etc., formerly in very common use, and not quite obsolete in the provinces, where Butty is now more generally heard. Bully-Bottom, a term applied to a courtesan, and hence an equivoque in Midsummer Night's Dream, act 3, scene 1 and act 4, scene 2, which has escaped the observation of the commentators."
When I was growing up in Ireland, "butty" was commonly used to mean a mate or friend. By the way thge meaning of the word "equivoke" is interesting in itself as it is given "as an expression capable of having more than one meaning; a pun." So even in Shakespeare's tim Bully had a variety of meanings.