England coach Trevor Bayliss admitted he faced some difficult selection decisions ahead of next month's Champions Trophy after the tournament hosts launched their preparations with a 2-0 series win at home to Ireland on Sunday.
England were in danger of falling short of 300 until Bairstow, ably assisted by Yorkshire colleague Adil Rashid (39) led a charge that saw 61 runs scored in the final four overs of an eventual total of 328 for six.
Sam Billings took the gloves in both Sunday's match and England's seven-wicket win over Ireland in Bristol on Friday in place of Jos Buttler, one of several England white-ball 'regulars' who missed the series because of their Indian Premier League commitments.
But Buttler, along with all-rounders Ben Stokes and Chris Woakes will be back from the IPL when England continue their Champions Trophy build-up with a three-match campaign at home to South Africa later this month.
"I think there's probably not a lot between the three keepers but the amount of runs Jonny scores, it'd be hard to leave him out," said Australian coach Bayliss.
"Every time we give him a go, he gets the job done for us."
And he made it clear he wanted to get into the Champions Trophy team, with England bidding to win their first major ODI tournament.
"It's something I've been targeting -- I want to be a part of every England side going forward," said Bairstow.
"We have a heck of a lot of talent in the group, but if I put in the performances then who knows?"
- 'X-factor' -
In the field, Durham fast bowler Mark Wood, returning from a third ankle operation, impressed with some lively overs against Ireland.
"Wood brings a bit of extra pace, he's got that X-factor -- he's our quickest bowler, he can get the ball to reverse as well and he can be hard to handle," said Bayliss.
Joe Root, one of five Yorkshire players in England's XI, was named man-of-the-match after making an elegant 73 during a partnership of 140 with captain Eoin Morgan (76) and then taking an ODI-best three for 52 with his handy off-spin.
"We're building momentum towards the Champions Trophy and this was another step towards that," said Root, England's new Test captain.
"We want to be put under pressure just before a major tournament, it'll be great to see how the lads respond (against South Africa)."
Ireland captain William Porterfield led from the front Sunday with 82 as the Test aspirants restored some pride after being shot out for a mere 126 in Bristol.
At Lord's, they were dismissed for 243 just 23 balls from the scheduled finish, having made life awkward for England prior to Bairstow's run-spree.
"I thought we were much improved today," said Porterfield, whose side face Bangladesh in Malahide on Friday in the start of a triangular one-day series also featuring New Zealand.
"We kept going while that big partnership was happening, we got (Root and Morgan) out, but Bairstow did well at the end and got them to a big total.
"And even with the bat, we were probably just a couple of wickets behind the game most of the way. If we had a couple more in hand at the end, we were in the game."