I'm not sure on the website with the regs. I do have a site where you can down load the forms you need to taking a gun in ( i'll pm that to you ) its off an outfitters site..so don't want to bend the rules and link it through here.

Ok couple of items for you to keep in mind.

1) unless you fill out the paper work for the rifle your outfitter is going to allow you to use, YOU CAN NOT have a firearm in canada. not only are you registering the firearm, but it is your lic to carry a firearm.

2) you possibly will be questioned on your return trip back into the states, where the weapon is you used to harvest the bear.

3) going back to item in one, if your checked by a game warden and your holding that rifle and you don't have your paper work. you, the guide and the outfitter could be in some hot water.

now the odds of having a game warden check you in the back country, slim. in 3 trips up to canada, we've only had the game wardens stop in camp once ( and that was in camp, not out in the stands or while fishing )

but the cost is around 35.00 bucks to register your rifle.
you go into customs, pick up your rifle, stand in line and present your paper work/ passport,gun paper work and pay the fees. they will give you a stamped copie of yourrifle paper work and a receipt and that will be what you carry with your hunting lic to be legal.

good luck on your trip.