I wouldn't do a full refinish for such a small gain. Try the tru oil over the small spots first. Lightly sand the areas with damage, apply a few coats of tru oil over the sanded spots. If you dont like the glossy look of tru oil then buff it lightly with 0000 steel wool, polish to satin sheen with any cloth readily available, piece of denim, golf towel etc.
A few more options would be to sand the rough areas lightLy along with lightly sanding whole bow to scuff the finish, then spray or wipe finish over the entire bow.
Tru oil is a very nice finish if the directions are followed but labor & time intensive.
Minwax spar urethane spray or wipe is very popular but takes some time to dry.
Krylon crystal clear spray is almost too easy. You can recoat with several light coats every few minutes and have a dry bow in a few hours.