I just finished making a purse cake, then as I was working on it I noticed it began to have air bubbles, then more and more. Why does this happen and how can I prevent this in the future and how can I correct this?

The general consensis(sp?) is that is caused when the fondant is not adheared to the cake well enough developing air tunnels. In other words you did not press the fondant onto the cake well.
Take a pin and make a tiny hole on the underside of the bubble; smooth the fondant down. HTH