Bairstow struck 13 fours and two sixes in his 88-ball display at Headingley on Tuesday and is expected to feature for Yorkshire's first-choice team next week.
The wicketkeeper-batsman had not played since suffering a freak injury on a golf course in September, which ruled him out of the 2022 Twenty20 World Cup and test series in Pakistan and New Zealand.
Yorkshire's 2nd XI coach Tom Smith said Bairstow was a "little bit nervous" ahead of the match but settled in quickly as he batted at number four.
"Once he got going, he looked like he'd never been away," said Smith after Yorkshire ended day one of the four-day contest on 437-7.
"Watching him towards the end, the way he plays the late cut, the way he drives the ball, the way he played the spinner, one shot over extra cover showed that international class."
The five-test Ashes series will begin at Edgbaston on June 16. England lost the previous edition 4-0 in Australia.
