The 24-year-old played his first full 90 minutes for Wales since his move to the Bernabeu in Saturday's 1-1 draw with Finland.
Bale's progress in Spain has been hindered by a series of niggling injuries, leading some to doubt whether he could make an impact in La Liga.
But his recent performances have seen him score three goals in his last four Real appearances and win praise in the Spanish press.
Bale has stated he is relishing being with one of the world's biggest clubs, and Coleman knows that enjoyment will inevitably lead to good performances.
"I've had a chat with him and asked him how life is in Madrid and he's enjoying it, enjoying his football and the players have been great with him.
"If you are comfortable in your environment and are content then you take that onto the pitch with you.
"Knowing the type of boy Gareth is, once he's happy then he will enjoy his football. He will get used to what's happening in and around him.
"He just wants to play football and be on the pitch."
And Coleman has praised Bale for remaining level-headed despite all the attention being lavished on him.
He said: "I've seen him this week and he is exactly the same boy. He is no different. There is no reason for him to change.
"He is a cracking lad to work with and he is no different to how he was six months ago."
The Dragons were on course for a morale-boosting win against the Finns thanks to Andy King's goal at Cardiff City Stadium, but were denied by a stoppage-time equaliser from Riku Riski.
It was not the ideal way for Coleman to mark the signing of his two-year contract extension, but a three-match unbeaten run gives him reason to be hopeful as Wales build towards the Euro 2016 qualifiers.
"I think I've seen enough in the last couple of camps," said Coleman. "People forget abut the players when there has been a lot of pressure and negativity, it is hard for the players walking onto the pitch, especially the way we play as we are quite patient in our build-up.
"I stand by the fact that in the whole World Cup campaign there were only two games we were not good enough in, both against Serbia, otherwise the players have had a go. I have seen a lot of positives.
"I am worried about the next three or four months in terms of a lack of action for myself. I don't like that but it is part of the job. But looking at this squad of players and the possibilities, I am quite optimistic.
"We will play again in March and we have some other options, but nothing concrete, and we will maybe two more games in the summer."