He also accepted a formal written warning.
With Ben Stokes already under investigation by police for an alleged assault that occurred in Bristol a couple of months ago, England find themselves in absolute turmoil.
Indeed, Sportsmail understand that Bancroft, who made his first Test half century at the Gabba, did not want the incident to come to light and has no issue with Bairstow, who is said to have apologised for any misunderstanding.
Fox Sports Australia is reporting Bairstow headbutted Bancroft, while other versions suggest it was more low key and a case of tomfoolery gone awry.
The England and Wales Cricket Board is investigating reports English batsman Jonny Bairstow headbutted Australian batsman Cameron Bancroft in Perth earlier this month.
England Test squad: Joe Root (c), James Anderson (vc), Moeen Ali, Jonny Bairstow, Jake Ball, Gary Ballance, Stuart Broad, Alastair Cook, Mason Crane, Tom Curran, Ben Foakes, Dawid Malan, Craig Overton, Ben Stokes, Mark Stoneman, James Vince, Chris Woakes.
They had arrived in Australia with questions having been raised, including by ex-England opener Michael Vaughan, about their team culture following the barrage of punches thrown by Stokes in the hours after a one-day worldwide against the West Indies in September.
Seamer Mitchell Starc, meanwhile, has confirmed that Australia would continue to target the fragility of England's tail as his side moved to the brink of a 1-0 lead in the five-match series on Sunday. "Following an initial conversation with Jonny Bairstow we understand the context and will follow up with England players and management after the Brisbane Test", an European Central Bank statement read.
Another source told Sportsmail 'Jonny is a rugby man and part of their culture is to bump heads if someone buys them a drink.
Whether the European Central Bank deem the Bairstow episode to be worthy of further action or not, it will inevitably lead to renewed questions about the freedom afforded to England players, particularly in light of the Stokes affair.
The players compiled a code of conduct at the start of this tour in an attempt to avoid any repeat of the Bristol incident that has cast such a cloud on this tour but at the same time management were determined to carry on treating the players as adults.