Kind of hard to tell you what to do without knowing what kind of finish the bow has and what condition it's in. Lacquer, polyurethane or one of the new catalyzed finishes? Gloss or satin? If it's lacquer or poly, you can run into compatibility issues. Putting a new gloss finish over the oldmight lift the old finish and make it crack and crinkle.

Best bet if the bow has a gloss finish to start with would be to try some good paste wax. Wax it up and buff it real good. If it had a satin finish, you could buff it down with some 0000 steel wool and then wax and polish it.

My ChekMate had a satin finish but I decided I wanted a gloss so, after the warranty expired,I sanded the old finish off and redid it with plain old Birchwood Casy TruOil.