1. Wrap the bass snugly in bubble wrap so it fits tight in
it's case or gig bag. You don't want it rattling around.
2. Get a box from your local Guitar Center that was used to
ship a bass to the store (they're happy to get rid of them)
3. Pad the inside of the box bottom before you slide the bass/case in.
4. insert padding, foam, styro-peanuts, crushed paper or
whatever else you have - all around the case inside the box - the goal being to protect it on all sides, and seal the
box tight with tape.
5. Write FRAGILE in big letters outside the box and THIS END UP with a big arrow pointing toward the headstock end.
(This keeps them from laying it flat and piling heavy things on top of it.)
6. Ship FedEx Ground - While other shippers bounce your packages around causing crushed corners, punctures, and
other damage, FedEx (in my experience) "babies" fragile
packages and delivers your bass in pristine condition.
Be sure to insure your bass for it's true value just in case.
I've shipped several and received several basses and guitars and speakers this way with absolutely no problems whatsoever. You can track your shipment with them online,
and it takes 2 to 5 days max for delivery.
As a bonus, FedEx Ground is cheaper than other shippers.