Stokes, 27, was acquitted on Tuesday and has reportedly apologised to his team-mates for the saga, but has not gone public.
Bayliss is hopeful his star all-rounder can mend some of the damage with a statement in the coming days.
When asked if he thinks Stokes should apologise, Bayliss said: "Certainly.
"I think it was important to actually apologise to the boys in the team, management of the team and management at the ECB, who had to go through a lot of extra activities to work our way through it."
On Stokes' call-up to the England squad for the Third Test against India, Bayliss said: "We’ve got the next two days to assess where he’s at.
What the experts say
Former England captain Michael Vaughan: “He has brought the game into disrepute. Knowing the England cricket fans as I do, they will give him a reception.
“I don’t think he deserves that. He’s certainly not a hero, as some have portrayed him to be.
“I do think he owes many an apology. The cricketing fans around Ben will cheer him and love him. But most away from cricket don’t see him in a great light at all. He has to win back quite a lot of people in terms of the perception of what he is.”
Ex-England skipper Nasser Hussain: "I think Stokes needs to have a long, hard look at himself – it's a couple of times now he has been in the press for the wrong reasons.
"The Ben I know and who I see around the cricket team is a popular, unassuming, down-to-earth, very pleasant individual that will stay after a game and do autographs with kids for an hour and give his time.
"But I only see Stokes at cricket, so Ben has to make a decision – the image we see of him at cricket is probably not the image that has been portrayed over the last six months in the newspapers."
Former England star Bob Willis: "Ben Stokes hould be given a yellow card, a final warning and told he must never again damage the image of cricket.
"But it is right that he is free to play in the Third Test on Saturday and, in my view, the disciplinary commission should not impose further sanctions.
"After all, Stokes has been found not guilty in a court of law. And I don’t think Stokes needs to perform a Tiger Woods-style public apology."
"It was a collective decision – myself, management, captain, the board, Ed Smith – everyone had a say.
"It was basically thought that for his own well-being it was good to get Ben back around the cricket.
"There's nothing automatic about selections, we'll see how he is mentally as well as physically.
"We'll find out over the next couple of days, I haven't actually spoken to him yet. We've got the next two days to assess where he's at.
"It's a good position to be in from that [a selection] point of view. We've got some guys in form, in the team.
"It will be a difficult decision to make. Whether it's Ben or someone else."
Bayliss went on to say England have learned their lesson from recent off-field issues.
He added: "Since the incident we've done a lot of work with team culture with the two captains – and that's ongoing. Changes with curfews and that type of thing.
"In the past all the other teams I've been involved with and this one, when I arrived, would treat teams like adults and [players] will respond like it.
"For a team on the road 11 months out of 12, we had an incident we'd rather have not happened to a degree and we've thought we needed to do something different.
"There were a couple of small indiscretions in Australia after that incident and I think the players have finally woken up.
"They've learned their lesson and the way they go about their profession has been top class."
The Third Test starts on Saturday at Trent Bridge, with England leading the five-match series 2-0.
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