Lately I have been shipping them in fishing rod shipping tubes. I got some from a friend at Dick's. These are thick, smaller diameter and much lighter than carpet tubes. These tubes only work for straight limb bows, not enough room for a recurve.
When I ship a bow I include a bill of sale with specs and the price with the bow, even if it is a freebie. I bought a book of sales slips, the kind with carbon paper, to make my bills look professional, I mark the bill "paid in full". I do this to establish value and never pad the bill to anything above what the bow is actually worth. I do add the shipping cost to the bows value, it the USPS trashes my bow I want them to pay me back for the shipping cost I incurred.
I have had one bow broken in half by the USPS, it was insured for the selling cost, the USPS settled my claim for the amount stated on the bill in a couple of weeks. The sales receipt enclosed with the bow made the claim ironclad. I have shipped over 50 bows with good luck from the USPS and Priority Mail so far.