If it's handgun ammo I wouldn't even try. They will think you have a hidden handgun. For Alaska take a shotgun, declare it, do the paperwork, pay the small fee, make sure you have the ammo stored separate from the gun, and you're good. You are wasting your time if you're taking a handgun for bears anyway...not enough firepower, bring a 12 gauge. Besides you are just as likely to run into a grizzly in northern BC or Alberta as you are in Alaska.