Green’s Dictionary of Slang

bully adj.3

(Aus.) euph. for bloody adj. (1); also as infix.

[Aus]Dead Bird (Sydney) 27 July 8/3: ‘Mustn’t smoke, mustn’t blank well smoke? Oh, J.H. C —t, here’s a go. I’m losing £500 as fast as I bully well can and I mustn’t smoke’.
[Aus]Dead Bird (Sydney) 27 July 8/4: ‘I’ll never write his blank name no more unless he starts with a dray tied to his tail, and Mr Jack Bully Lucas on his back’.