I have never traveled out of country or went through customs with a bow but I have flown a lot here in the states with one and really have never had much of an issue. I bought a hard bow case. Even though it has a foam lining in it I still stuff clothes around the bow to help cushion any shock it might see, like airline workers throwing it up on a rack. The locks on the bow case are kind of cheesy and probably wouldn't take much to open them but I still think it helps to keep people out of it. I often put my knives, rangefinder, and other expensive items in with the bow also. The locks make me feel a little better about it.
The big thing you will need to know is your bow will not show up with the rest of your luggage, so don't panic when it doesn't show up on the conveyer. It will be considered oversized and go to a special room they have for over sized luggage. I notice golf clubs are about the number one item that end up in the same place. I always wait to get my luggage and then go find the oversize room or office that will have the bow. Usually it is there waiting for me. Hope this helps.
GBA