The pair repeatedly tussled for the final podium spot during Saturday’s race, with Prema driver Bearman running ahead for much of the race.
They were running behind Isack Hadjar (Hitech) when they first came to blows, with Virtuosi driver Doohan going off at the exit of Stowe and calling for Bearman to be penalised for pushing him off.
But the Ferrari junior pushed on, passing Hadjar up the inside of Copse before Doohan followed suit the following lap to reignite their battle.
By lap 17, the pair had gotten ever closer, with Bearman eventually running wide at Vale as Doohan went through for third, appearing to wave as he did so.
Asked after the race about the wave, Doohan said: “I think it was probably my 13th time trying to get past him and he pushed me all the way out onto the double kerb on the exit of Turn 15 under braking, which isn’t allowed.
“He swerved at me under braking into Turn 15 and to his disappointment locked up, clearly by turning under braking, especially under these conditions, isn’t going to be too great especially when there’s a driver on the inside, [so he] locked up and went off.
“I just did a little wave because I felt karma had come back and unfortunately he lost out.
“We had a gap behind us so potentially he could have slotted into P4 but he lost positions. So I said au revoir my friend and see you later.”
Saturday’s race marked Doohan’s first podium since Saudi Arabia, where he finished second in the feature race.
He has suffered a difficult year and currently sits ninth in the standings, having impressed in 2022 with three wins and six podiums to finish sixth overall.
Although he stopped short of calling for Bearman to receive a penalty, Doohan said his rival’s driving was “definitely not up to my standard I would say,” and said he would let the stewards decide whether further action was necessary.
Discussing the incident, Doohan said the fight for third “didn’t go as smoothly as I’d hoped”, adding: “Not really the racing standard that I was hoping for, what I got, and I really had to be very smart because if I wanted to commit to any of those moves, I probably wouldn’t be sitting here right now, I’d probably be in the gravel trap.
“Luckily in the end, he was trying to close the door on me but ended up making a mistake, so I was able to get past with no damage, which was nice.
“I could see my pace immediately jump by 2.5s a lap, what I had the whole time, just unfortunately it wasn’t as easy to get past as I’d have liked.
“How he drives his car is up to him, obviously. I will let the stewards pick that up really.
“But occasionally, by the time I’d get to the exit, I wouldn’t be exactly alongside because mid-corner when I’d get alongside, he would have a snap and go to crash into me, so I’d have to get out, and then he’d think it’s acceptable to push me again off track.
“So that is not really the standard I choose to drive by, but he’s a racing driver and he’s fighting for a podium position, so I'm not saying I wouldn’t expect anything less but maybe a little bit cleaner next time.”
