Bale was thrust into super-stardom this summer when he became the most expensive footballer in history courtesy of a £85m move from Tottenham Hotspur to Spanish giants Real Madrid.
Much of the 24-year-old's time since the move has been spent with the Wales squad, and Coleman has been taken aback by the increased interest surrounding the player.
"I am not used to this to be honest with you. Having a player like that," Coleman told PA.
"I managed Fulham with some good players but none of them went for £85m. I can understand the frenzy that comes with that and I have to get used to that - we all have.
"There are people coming out of the woodwork wanting to see him and have an autograph. We have to tighten up on everything and how we look at it. But I would rather have that problem than not - it means he is playing for us."
Wales will face Serbia in a World Cup qualifying match tomorrow night as they look to avenge their 6-1 defeat in the reverse fixture last year.