Alex Hales says England had their sights on a score of 500 during their ODI-record total of 481-6 against Australia at Trent Bridge.
Hales smashed 147 from 92 balls with Bairstow hitting 139 from the same number of deliveries as England surged past the previous record of 444, that they had set against Pakistan in 2016, also at Nottingham.
Jason Roy made 82 while Eoin Morgan (67) hit England's fastest one-day fifty, getting there from just 21 balls, and overtook Ian Bell as the country's leading run-scorer in ODIs.
It was shortly after Morgan's arrival at the crease, with England on 335-3 in the 38th over, that the prospect of reaching 500 was discussed.
"There was a moment when Morgs came out but we didn't quite get there unfortunately," Hales said of targeting 500. "He was saying 'if ever there is a chance, now is it' but I just couldn't quite get going at the end with those wide slower balls… but what a day!"
Bairstow confirmed that similar conversations were being had in the dressing room: "When Morgs got going with Baz it was definitely something that the lads were thinking about!"
As it was England had to settle for merely smashing their own world record while Bairstow was able to celebrate scoring his fourth ODI hundred in six innings.
"It was amazing," he said. "This ground is a special ground for us, it always seems to bring something exciting and what a pitch! Really, really good fun out there.
"I've got no idea (what the secret to scoring hundreds is), to be honest with you. It's just a case of relaxing and watching the ball.
"Each opposition gives you different challenges, each bowler is going to give you different challenges - you look at Stanlake at 6ft8in compared to Richardson who is smaller, skiddier. It's a case of maintaining your consistency, doing your same things day after day and keeping enjoying it, that's exactly what I'm doing at the moment."
Meanwhile for Hales, it was a timely century as he battles to try and keep his place in the side when Ben Stokes returns from injury.
"I'd say a little bit of both [excitement and relief], probably more excitement," he added. "As Jonny says, what a ground! We've had some great memories here as a team: chasing 380 against New Zealand and setting the previous record, which was done here as well. Great memories and today is another special day.
"[My plan was] just to keep the momentum going, I've got enough experience playing here to know it's a good pitch and a fast-scoring ground. It was good to come in and get off to a decent start, build a partnership with Jonny and it gave us a real platform to do something special."
Watch the fourth ODI between England and Australia from 1.30pm, Thursday on Sky Sports Cricket.
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