Use water (or oil) with the steel wool and it will scratch a bit less, especially if you buff lightly. You can get the finish relatively glossy if you lightly buff down thru the gauges of steel wool or sand paper. You can finish with oil and rotten stone and a pad if you want to go that far. or put on a nice coat of car wax over your scratches and see if they kinda go away. It will also help keep out moisture.
If the scratches are not so bad, I would just wax over it, unless you happen to know exactly what finish was used in the first place, in which case you can apply another coat over the bow.
Later
ChuckC