What's best for a period finish? That's a bit hard to say. The Maximilian I bows at the Kunsthistoriches Museum in Vienna are a dark red with gold lettering. I suspect it's a red lacquer.
Many bows are just dark wood now and it's hard to tell what they were made with. Some bows, like the Fels Colonna Bow in the Wallace Collection (London) are covered in bone plaques. That doesn't help much either.
I prefer to give my bows a coat of linseed oil to bring out the color. Then wait a couple of days, buff with some very fine steel wool, and rub in a coat of tung-oil. Let that soak in a day or two, buff again and give it another coat of tung oil. If you stop after two or three coats, you'll have a nice, natural looking finish. Add another coat and the tung oil will start getting a bit glossy. If you do 5 or 6 coats, the finish will go very bright and glossy indeed. If you look at the Ulrich V bow in the Metropolitan Museum (New York) you'll notice the finish is surprisingly glossy after 500 years. It was probably brighter when new @ 1460.
I prefer a flatter finish for my projects, while my apprentice, Lightly, likes 'em glossy. What's best 'period' practice? I really don't know, but 2 or 3 coats of tung oil certainly looks nice and it keeps the wood clean and fresh looking for a long time. Geezer