Cole called the FA a "bunch of t***s" on Twitter after he was accused of "evolving" his statement supporting Terry's defence against the charge he racially abused Anton Ferdinand.
Speaking to the BBC, Bernstein said the player had followed up his personal apology to go with an official one. "He apologised immediately on Friday and he came to see me last night and apologised to me personally,' said Bernstein. "He showed real contrition. He said he was really sorry.
"He is free to play for England over the coming matches. It is up to the manager to decide whether he plays or not."
Bernstein also suggested that Cole, who stands on 98 caps, is unlikely to be England captain when he wins his 100th cap.
The apology seems to leave the door open for the Chelsea and England defender to play in the World Cup qualifiers against San Marino and Poland with Bernstein confirming that the final decision on the player's selection rests with manager Roy Hodgson.
Cole was yesterday charged with misconduct by the FA over the well-publicised Twitter comment, and is facing FA disciplinary action after he reacted furiously on Twitter to doubts being expressed about his evidence in the John Terry racial abuse case.
The FA released a short statement in response to the comments made by the player.
"Chelsea FC’s Ashley Cole has been charged by The FA in relation to a Twitter comment which was improper and/or brought the game into disrepute. Cole has until 4pm on Thursday 11 October 2012 to respond to the charge."
The Chelsea left-back is in Roy Hodgson's squad for the World Cup qualifiers against San Marino and Poland but some pundits, such as former England striker Alan Shearer, have called for Cole to be banned.
Shearer told the BBC: "I think the FA can put a big statement out here by not fining him but actually banning him on Friday against San Marino."
Cole responded by retweeting a comment on Twitter which referenced an incident in the game between Newcastle and Leicester in 1998 when the former Magpies forward's boot made contact with Neil Lennon's face.
The FA ruled the striker had been making a "genuine attempt to free himself" from a tangle with his opponent and took no disciplinary action against him.
Cole retweeted a post from @CollinR4 which read: "Alan Shearer says @TheRealAC3 needs to be banned for comments. I want his opinion on bans for kicking Neil Lennon in the head. #GlassHouses"
Cole has spoken to Hodgson and will meet up with the squad at the new national football centre, St George's Park near Burton-upon-Trent.
It is understood that if he is left out of the San Marino match it will be a case of Hodgson resting players against the Group H minnows rather than any statement relating to the controversy that erupted on Friday. Cole, 31, has 98 England caps to his name and will be desperate to reach the 100-mark.
He will also be part of the England squad that assemble at St George's Park for the official opening today by the Duke and Duchess of Cambridge, William and Kate.