I don't know too much about refinishing, so some others may be more help. But, I just did a refinish on a vintage bow.
What I did was sand all the finish off down to bare wood and glass (sand very lightly on the glass ... I did this with 220grit and steel wool).
Then I sanded the wood through the grits up to 320 or 400 or so and sealed all the wood and the sides of the limbs with CA glue.
Then I lightly sanded the CA once it dried, did another quick coat, sanded with 320grit, then sprayed it with rattle can lacquer.
It came out pretty nice. The superglue really brought out the grain.
I think most of those older bows have a catalyzed varnish or catalyzed poly finish on them, so you'd have to find a compatible finish.
If you just wanna put some finish over what you've got you'll almost certainly need to lightly sand the surface so the finish adheres well.
Also, Bow Hospital is supposed to be good, they charge a bit, but it should come out really nice and last a long long time.