Green’s Dictionary of Slang

1. vigorously, enthusiastically.

1904

Argus (Melbourne) 4 June 5/8: ‘How did I barrack, eh?’ I say gleefully to my son. ‘You barracked a bonza,’ he answers, ‘but there were moments when I was ashamed of you!’.

2. (Aus.) to a great extent; very well, as in phr. go bonzer.

1907		Examiner (Launceston, Tas.) 21 Nov. 7/5: November 11, noon. – Going ‘bonzer’; time card looking healthy.
1914		‘B. Cable’ By Blow and Kiss 246: Came back grinning widely, with the assurance that it was coming down ‘Bonzer’.
1926		Brisbane Courier 7 Oct. 12/3: Of such are those who loudly proclaimed a book, or a holiday, or a meal, ‘goodo!’ [...] and who have informed me, speaking of an examination, that they ‘done bonzer in English’.
1931		Western Mail (Perth) 19 Feb. 2/2: Th ‘stoo’ fickened up bonza. It smelt bonza.
1933		Listening Post (Perth) 26 May 18/3: Anyway, a good muster of Jandakot, as well as Spearwood, diggers put in an appearance, and everything went bonzer.
1941		Dly News (Perth) 8 Mar. 7/2: Everything was going bonzer and peaceful, and I was beginning to wonder whether the old chap wasn’t mellowing with age.
1963–74		B. Humphries Barry McKenzie [comic strip] in Complete Barry McKenzie (1988) 24: I reckon the old song went over real bonzer!

3. substantially.

1911

Sun (Sydney) 28 Aug. 9/5: That new piano was busted to smithereens; we’d cut bonzer big holes in the new drop-curtain, an’ smashed every stick of furniture in the place.