Hi John
I've shipped loads of basses over the years all around the world. I think it's actually pretty simple once you get going.
As you have the original case, just get a couple of big boxes from your local guitar store (ideally bass, but guitar work okay if you put them end on end) and double skin it in them with lots of packing tape. Then just comapre a few costs from the various couriers (UPS, FedEx, DPD etc.) and make sure you ship it for the appropriate value, and ideally use a trackable service.
Cheers
Gareth