Bumrah stood in as captain for Rohit Sharma, who missed the opener due to the birth of his second child, leading the tourists to a stunning 295-run victory on day four.
At the break on day four, Australia were 104-5 with a defiant Travis Head not out 63 and Mitchell Marsh on five as they chase a near insurmountable 534 to win.
The Pakistan-born opener was reprimanded by cricket's global governing body on Thursday for wearing the armband during the 360-run win over Pakistan in the series-opener in Perth.
"Any sort of moment you can get to have a few days or a week just to get away from the game and get your mental side back to a position where you can go out and perform internationally, it's important," he said.
