The best way to ship a bass (IMHO) is in a hard shell case. If it's a good, form-fitted case, there's really no other packing necessary; just find a box that it fits in and you're good to go. You can wrap the case with bubble wrap or fill the box with peanuts if you want, but if you aren't concerned about the outside of the case getting dinged or scratched, you don't need to bother. If the case isn't form-fitted and the bass is loose inside it, you probably want to use some bubble wrap or something to secure the bass inside.
It's possible to ship a bass safely in a gig bag. I've done it, but you really have to be careful about packing. Get a big, sturdy box, stick some extra sheets of cardboard in there to stiffen the sides, and use a lot of packing peanuts. If the bass has a bolt-on neck, you may want to consider removing the neck for shipping. You can use a smaller (cheaper) box, and there's less leverage to break something if it does get run over or dropped.
I usually find Fedex ground to be the cheapest, but UPS isn't too bad.
To get a box, you can:
- Google "guitar box" and you'll find companies that sell them; they usually come in packs of 5 so this may be impractical unless you're selling a whole collection
- go to your local music store and ask if they'll give you a box
- check the dumpster behind your local furniture store and hope you get lucky
- buy another bass on TB classifieds and use the box it comes in
