Best and cheapest do not go hand in hand. Cheapest usually equals a damaged bow for the recipient, so don't cheap out on packaging. I would agree that PVC pipe is the way to go (assuming it's not a recurve). Not sure about down in the states, but I don't trust the postal workers or couriers one bit up here in Canada. Fedex is actually cheaper than the postal service up here. You can check the cost and delivery times online for couriers such as Fedex, Purolator, etc.
On a side note - if you ever have to send something to Canada, your recipient will be very appreciative is you choose anything other than UPS. Their brokerage fees are insane.