My suggestion: simply using it regularly might do the trick. The opening and closing, putting things in and taking them out, would help. After all, if not using it has caused it to smell a bit whiffy, then the opposite - namely, using it - should shift the smell.
I've had good luck with either ground coffee or coffee beans (all dry, of course) in a cheesecloth bag placed in the handbag... removes mustiness and leaves a pleasant 'coffee house' fragrance...