I HAVE received earrings that were shipped "naked", and the posts DID poke through. You need to wrap them.
Bubble should be fine to ship - depending on how thick the item is on the stud. As above, a box shouldn't normally be necessary, but you do need to wrap them in something - depending on its fragility (and how much you trust the posties not to dance on it). That might make it too thick for the lowest shipping price.
Just a thought (I haven't actually tried it), but you could embed the posts in a sheet of cardboard or styrofoam - just thick enough to fully accommodate the posts - so they won't pierce through the envelope.
Good luck!