I just sent at least 3 dozen to someone. If you pack them tightly enough they don't move at all and then any damage would be if another box drops onto your and causes any dents. I didn't bubble wrap anything. I laid down a sheet of wrap on the bottom, then packed all the soap in tightly. I put in packing peanuts- really packed them in to any gaps in the sides, layer of bubble wrap on the top or packing peanuts if there is more room than a sheet will fill. Before I sealed the top, I closed it by hand and then shook the package like mad to see if I detected any movement or shifting in there. If there is, more packing peanuts until I can shake that package like crazy and nothing moves. Then seal her up!
Also, I got at least 3 dozen bars into a regional rate B box. You can ship up to 20 pounds I believe and it might cost around $10-12 depending on how far you are shipping. I was shipping within my state and it cost $6.16!