For shipping a guitar/bass only - the key is keeping the box as small/efficient/protective as possible. Oversized = $$$. Then it's two layers of heavy cardboard - reversed bias to form the box. Then it's bubble-wrap - the bigger bubbles the better. It should surround the bass like a pillow and fill the inside of the box.
A bass w/HSC doesn't require as much exterior padding - I've received a bass shipped in a HSC w/o box! (case taped shut) I would never do that, but the bass inside the case should be surrounded by bubble-wrap (small bubble version) and especially if the bass is not a tight fit in the case. Detune strings at lease a half-step and have a thin piece of foam sheet between the strings, fb & pu’s. Make sure nothing moves inside the case once it is closed.
Not a 100% guarantee it will arrive safely (I have stories...) but doing this will give it the best chance of getting to where you send it unscathed for the least amount of money. Oh, and always insure it for replacement value - always.