Bird, Michell Johnson and Peter Siddle each took a wicket in the first session as Sri Lanka struggled early after winning the toss and electing to bat.
But experienced Kumar Sangakkara has steadied the ship for the visitors just before lunch, unbeaten on 43.
Sangarakkara became the 11th player to pass the 10,000 Test run milestone.
Australian captain Michael Clarke is playing, saying he is 100 per cent fit following a hamstring complaint.
Bird dismissed Sri Lankan opener Dimuth Karunaratne for five in his second over caught behind by Matthew Wade after Sri Lanka won the toss and decided to bat.
Australia named skipper Michael Clarke to play in the Boxing Day Test against Sri Lanka at the MCG, while Sri Lanka elected to bat after winning the toss.
Sri Lanka captain Mahela Jayawardene chose to bat first in sunny conditions on a drop-in pitch which appears to have a light covering of grass.
Clarke, 31, is the leading runscorer in Tests in 2012 and needs another 56 runs to beat Ricky Ponting’s national record of 1544 which Ponting set in 2005.
Australia lead the three-Test series one-nil.
The match is due to start at 1030 eastern daylight time.
Australia fast bowler Jackson Bird made his debut and left-arm quick Mitchell Johnson has been recalled for Mitchell Starc (rested) and Ben Hilfenhaus (side strain).
Sri Lanka have included Dhammika Prasad for injured quick Nuwan Kulasekara who has a sore rib.
“I’d call myself 100 per cent (fit),” Clarke told the Nine Network at the coin toss on Wednesday.
“If I couldn’t have turned up today and performed at my best, I wouldn’t have been playing.
“The hamstring feels great and I’m looking forward to this Test match.”
Clarke admitted he would have batted first if he’d won the toss.
Sri Lanka skipper Jayawardene says the prospect of an excellent wicket prompted his decision.
“Brilliant conditions, looks a great wicket, and brilliant weather,” he said.
Teams:
Australia: Michael Clarke (capt), Ed Cowan, David Warner, Phil Hughes, Shane Watson, Mike Hussey, Matthew Wade, Mitchell Johnson, Peter Siddle, Nathan Lyon, Jackson Bird.
Sri Lanka: Mahela Jayawardene (capt), Dimuth Karunaratne, Tillakaratne Dilshan, Kumar Sangakkara, Thilan Samaraweera, Angelo Mathews, Prasanna Jayawardene, Dhammika Prasad, Chanaka Welegedara, Shaminda Eranga, Rangana Herath.