The pair have had a running battle, with Adam branded a "coward" by Bale last year after a clash in a pre-season game while he was still with Liverpool.
"There's no problem," said Adam, before joking: "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.
"We've moved on from all that. His career has blossomed and he is playing at the top of his game."