I ship a lot of small stuff USPS but never anything as big as a bass. I have however had a big combo amp and two basses shipped to me VIA the USPS and never had any issues.
As far as claims go, I've filed a few with USPS over the years and to my surprise, every time they were handled in a timely and professional manner.
Just idle curiosity, what happened to your bass?
"Strictly speaking, there is no certainty, there are only people who are certain." -anon-