Rohit was batting on 57 at stumps with Ajinkya Rahane on one at the other end with India eyeing a handy first-innings lead.
Bumrah, who missed the final Test of the Australian tour, is the favourite to share the new ball along with veteran pacer Ishant Sharma in the Test series against England which begins at Chennai on Friday.
As India prepare for fourth and final Brisbane Test with the series tied 1-1, the team resembles a mini-hospital and coach Ravi Shastri and skipper Ajinkya Rahane would be be at their wits' end to put together a fit eleven.
Bumrah, key to India's attack, sustained the strain during the drawn third Test in Sydney.
According to BCCI sources, Siraj was allegedly referred to as a "monkey" by a drunk spectator in one of stands at the Sydney Cricket Ground.
It was a gamble by the Indian think tank to make Bumrah the nightwatchman with wicketkeeper Saha and all-rounder Ashwin in their ranks.
The Indian skipper lavished praise on the marauding Hardik Pandya's "raw talent".
Australia 'A' were bowled out for 108 in reply to India's first innings total of 194.
Green was later withdrawn from the match with batsman Patrick Rowe named as the concussion replacement.
Srinath said that the dependence on spinners was so high that he had to often ask the captain to be given the ball.