Bubble wrap is great for protecting delicate stuff against high
accelerations. I.e., the box being dropped, thrown, etc. You don't
need that - you need protection against the box being "violated".
Bubble wrap will do that, but so will a couple of layers of cardboard.

Yes. I ship finely polished brass parts every day, and don't ever buy packing material. Fortunately, I share a courtyard with a bathroom supply wholesaler, so I have an unlimited supply of corrugated cardboard. I wrap the parts in tissue paper, then kitchen plastic wrap, and then however much free cardboard I deem necessary for the job.