Bairstow took off his helmet and knocked it against his head several times after he reached three figures in Perth to bolster England's first innings of 403.
The 28-year-old, who scored 119, found himself in the firing line earlier in the series after it came to light that he had greeted Australia's Cameron Bancroft by bumping heads in a Perth bar.
"It was a bit of light-hearted fun with everything that has gone on and that is exactly how it should be taken," he said, referring to Friday's celebration.
"The hundred in many ways was my favourite one, it meant a huge amount," he said.
Also Read
"I have played in a few Ashes series. Now to score an Ashes hundred is something you dream about as a kid.
"You want to say to your kids that you made an Ashes hundred at the WACA away from home.
"It has eluded me until now and it was a whole heap of emotions that came running through."
Disclaimer: No Business Standard Journalist was involved in creation of this content