Worth it to Service

I have a Bambino that I received as a gift perhaps seven years ago (roughly). It has begun running fast. I keep it in a watch winder and it gains a few minutes over a week or two. I was wondering whether it’s worth it to have it serviced. I like the watch, but similar models are available new in the $300 range. I have never had an automatic watch serviced before and don’t know the cost range. (I am in the U.S.A.) Thanks very much.