The Scotland international had previously been labelled a "coward" by the Tottenham and Wales winger, having injured him in tackles on two separate occasions
Tottenham wideman Bale was sidelined with ligament damage in May 2011 after coming off worse from a challenge with then-Blackpool star during a Premier League clash.
And the row escalated after Adam caught the 23-year-old with a similarly late tackle during Spurs' pre-season game against Liverpool prior to his move to Stoke.
|15/4||Charlie Adam is 15/4 to score anytime against Wales with Bet365|
"There's no problem," Adam told the Daily Mail. "I let him [Bale] score the last time, so things should be OK.
"I never spoke to him. We did speak during the game when we played them in Wales and, like I say, there's no problem. These things happen.
"We've had two incidents. But he's a top player. He could go on to one of the top clubs in the world.
"He plays for a great club in Tottenham, but he could go to Barcelona, Real Madrid or Manchester United easily.
"We've moved on from all that. His career has blossomed and he is playing at the top of his game. He's going to be dangerous on Friday night but, hopefully, we can cause them a lot of problems ourselves.
"He is a top player and I respect that. I don't have any grudges. He is one of these players that you want to play against.
"He is one of the select few in the world at the moment who are at the top of their game. It's a joy to watch him. Hopefully, he's quiet on Friday and we win."
Adam also revealed his frustration at claims that he lacked commitment during Scotland's 2-1 loss at the hands of Wales this season, a game which saw Bale net the winner.
"That was the biggest thing — people saying I didn't care. I was as gutted as anybody after the game. I do care," he stated.
"There is probably no one more excited about joining up and playing for their country as me. The criticism was there and I take it on the chin. Maybe it was my fault, maybe it wasn't.
"There are not many players in the world who could have done what Gareth Bale did that night. He got the ball, dribbled past me and stuck it in the top corner. The criticism is part and parcel of football and I understand that.
"He got the ball on the halfway line and I let him come to me. I showed him on to his left side - maybe I should have shown him on to his right. But he was 35 yards out and normally they go into the goalie's hands or go over the bar.
"It went into the top corner and I got the criticism. Maybe I could have got over a bit quicker and shown him down the line. But when you show him to his left, you’re not expecting him to hit it into the top corner.
"It's done, dusted and gone now. Let's just worry about the game on Friday night."