Definitely use a box not a tube. I have read war stories about how the tubes fall off conveyor belt and become targets for forklift drivers.
I go to an appliance store and ask for a refrigerator box. They're heavy cardboard and you can score one side where you want to make the folds. I also use pieces of a foam "pool noodle to protect the tips and wrap it in bubble wrap. You can also cut some spacers to support the inside of the box, but I've found the cardboard to be plenty stiff without it. I've shipped about 6 or 8 60" to 64" recurve this way with no problems.