If the hole isn't too small, you may get a plug-cutter bit the size you need to plug the hole. It cuts out dowel plugs. The advantage of using one is so you can cut out from the face grain, not like end grain in a dowel. Find a wood of similar grain, color and texture, cut the plug and glue in. Be sure to align the plug's grain with the bow's grain. Then sand, stain and seal accordingly.
Obviously more involved with this method. Even with this procedure, you may still see the circle outline of the hole, but not nearly as much.