The home side went to stumps on 95-4 with Bavuma 41 not out after only 30.4 overs were possible in Gqeberha after heavy rain and a wet outfield saw the play only start 15:45 local time and 30 overs possible before close of play.
After resuming on 20-2 after 12.2 overs after another rain-shortened first day, the Proteas lost debutant Marques Ackerman, caught behind off seamer Scott Boland who picked up his third wicket of the innings with the left-handed batter out for 6 from 38 balls.
Matthew Breetzke walked to crease after being jettisoned into the Proteas team after teh first Test defeat, but only lasted 17 deliveries to score four before playing a loose stroke off left-arm paceman Mitchell Starc to be cught by wicketkeeper Alex Carey.
The Proteas were in deep trouble at 40-4 but Bavuma and Ryan Rickelton stitched together a 52-run partnership for the fifth wicket, showing good battling characteristics, although Ricketon was dropped by Marnus Labuschagne when on 26.
The spilling of a fairly simple opportunity did not cost Australia too much though as Boland once again proved to be a thorn as the seamer had Rickelton (31) brilliantly caught at first slip by Matt Renshaw, taking a spectacular one-handed catch diving to his right.
Bavuma was showing a excellent application and technical capabilities to battle the world-class Australia bowling attack, and the skipper will carry the hopes of nation on his shoulders when he resumes on day three.