Green’s Dictionary of Slang

(Aus.) to construct a cigarette from cigarette ends.

1968		D. O’Grady Bottle of Sandwiches 30: Hope he brings the makin’s we asked him to. Smokin’ bumpers is all right when there’s nothin’ else, but by tomorrow we’ll be bumperin’ the bumpers.
1978		T. Davies More Aus. Nicknames 34: As soon as he came into the danger area they would have to bumper their cigarettes [AND].