I've never tried this but it seems like it'd work.
Montana Scabbard I've never liked the idea of carrying the bow up on the handlebars, getting in narrow single track is hairy enough as it is.
Me? I just use a pack and strap the bow to the pack, I have been known strap the pack and bow to a rear rack, too. It actually works better.
BTW, do a search on here for bikes, bicycles, there have been quite a few threads.
Carying an animal on a bike is a lot easier than it sounds and a LOT easier than dragging one.