Green’s Dictionary of Slang

(Aus.) a white man, often old and impoverished, who pursues Aboriginal women for sex.

1975		R. Beilby Brown Land Crying 210: He had the weird certainty that he must match her coarseness if he was to hold her. ‘So what your price, Myra—same as the bunji-men?’ [Simes:DLSS].
1981		A. Weller Day of the Dog 54: You better not be givin’ that ole bunji man a bit on the side when the Pretty Boy’s not ’ere.
1985		Nat. Times (Sydney) 12 Apr. 20/2: [T]he term, widely used by Aboriginal people around Perth, refers to lonely, alcoholic, old white men who wander the parks and back streets seeking ‘black velvet’—sexual solace from Aboriginal women. The best free translation of Bunji is ‘dirty old man’ [Simes:DLSS].
2014		P. Docker Sweet One [ebook] Cabbies have a rep. What rep? Bunji-men. What's a bunji-man? Goes in for the black girls.