The simplest solution that I've come across is to buy one of the, relatively, cheap bow cases at Wally World or one of the sporting goods chain stores. These are basically no frills, plastic cases with foam padding on the inside. Put the bow in it, secure the outside locking points with zip ties, wrap some frustrating packing tape around it and ship the entire thing. UPS and FedEx both will ship that way. I"ve done it twice so far and have one coming to me that way as well.
The toughest shipping for a bow was finding a safe way to pack a 69" longbow for mailing. I used some plastic carpet tube that the guys at Home Depot gave me. They save them and usually have a few standing up somewhere in the back. Cut to a shorter size, these would also make a great way to transport arrows. Hmmmm.
Hope this helps,
Doc