Interesting. The usage seems to me "mock-Irish", for lack of a better term. In that context, it may be worth noting that "buille" (pronounced roughly bwill-eh is an Irish word for a blow or strike.

The only other possible connection I can come with is that the word "billy" was used for a stylish necktie or cravat (19C.), apparently. That may tie in with the first example, so to speak.

Regards