I'm assuming that this is a wood bow and not a glass one? I've refinished wood bows like that before. You might wait for others to chime in, but I refinished it just like any other piece of wood. Take down the finish with sandpaper, just try not to take off too much wood in the process (you might change the tiller), then refinish with a few coats of poly, boiled linseed oil, tung oil, whatever. If you do find cracks in the wood itself, take real good care of them before you do any refinishing.