When I went to Canada (94) they asked if I had any firearms. I said no, I had a bow. He wasn't too concerned about it. Did ask me why and I told him. Now my wife and 3 year old daugheter were following me in another car and in the next line (overnight type vacation before I kept going north) and her customs agent grilled her. Wouldn't believe I would hunt bear with a bow. Said they were too big and you couldn't kill one with a bow. I must have a gun in my car. Finally he let her go. Point is it depends on what agent you get as to the amount of hassle.
Oh, by the way, make sure you let the agent know you have a bear when you come back into the states so you can get the export papers. Otherwise they make you turn around and everyone knows you as the "bear man".