To ship a bow safely, you must make sure it is properly protected. My favorite way to securely ship a bow is to put it first inside a PVC plastic tube, and then inside a triangular shipping tube.
Go to Home Depot, or some other sort of building materials store, and purchase a 34" length of 1 1/2" or 2" PVC schedule 40 or SDR 21 ( 3/16") with two 1 1/2" or 2" matching size slip-on caps. You can usually get someone at the hardware store to cut the pipe to length for you.
Put a bit of crumpled paper inside one cap, and slip and twist that cap onto one end of your tube. It's necessary to provide some sort of padding inside the caps so that your bow doesn't rattle back and forth and break the tip in transit.