Bale has twice been injured as a result of challenges from Adam, which led to Bale branding Adam "a coward", but the Stoke City midfielder has insisted that he hopes that they can move on from the two incidents.
Adam said: "What happened in the past has happened. I apologised to him during the game, after a corner.
"I said to him I was sorry and thought everything was alright. I also apologised to the manager of Tottenham at half-time.
"Then all of a sudden, I was being called a coward. That's football and it won't stop me tackling and trying to be the player I am. I hope it is done and dusted now."
Wales host Scotland on Friday evening as both sides look to earn their first win of their 2014 World Cup qualifying campaign.