I echo everyone else's opinions about letting the wood dry.
But back to poly-you're-insane. Go for the low gloss or satin. Apply sparingly, allow lots of time for it to cure, touch it up lightly with very fine steel wool between coats, and add lots of coats. Then when you have about a dozen coats on, touch it up again with the fine steel wool to take off any remaining gloss for a nice matte finish. In late winter when you are done hunting for the year and before spring comes with moisture, add a couple more coats of poly, finishing off with that steel wool again. It makes for a durable surface that to some degree discourages the wood from picking up moisture (no finish seals really out humidity).
That's if you want a matte finish for hunting, glossy bows scare game. But if you are building a bow for a target shooter or a wall hanger for a friend that just wants to show off your bows go all in for the glossiest finish you can make!
Nothing catches the eye of a non-primitive archer than shiny things!!! For some reason matte finishes turn them off. Make it look like plastic and they don't feel so scared.