Good for you on your hunt. I leave in two days to New Brunswick.
Go to
http://www.rcmp-grc.gc.ca/cfp-pcaf/f...om/909-eng.htm
for importation regulations for your rifle. I am not sure what is required for the bow. You complete the pdf form ahead of time and bring it with you. Rifles must be in a case, with trigger locks. No ammo with the guns. big no no.
Register your firearms with U.S. customs ahead of time. Look in your local phone book for the closest, and just give them a call for a convenient time. You must do this before your trip. They are good people, easy to deal with...no cost.
I would call your airliine and find out what they require for your gun and bow, then be sure to get a copy of thier regulations in writing. Airlines vary alot with rules, and you want to follow them closely. Once you know the rules, (like the canadian permit) it is very easy and not much of a hassle at all. I have allways found the Canadians very easy and pleasant to deal with, when you respect their rules.