If the stringing is tight, do not pack the doll seated, find or make a box long enough to ship standing. If the stringing is very loose or if it is a soft body doll, go ahead and pack them seated.
Lift head of a strung doll away from the body and wrap tissue around the neck firmly making sure the tissue buffers the body from the head.
Bisque head dolls (especially bisque), Still the eyes of an antique bisque doll in an open position by packing inside the head with tissue or cloth.. even if the eyes are not sleep eyes, pack the head. This can prevent the plaster giving way and the eyes falling out to rattle around and possibly break or chip the head. If you can not get in through an open pate, you can pack with a long strip of cloth through the neck.
For dolls of composition, hard plastic or other materials with weighted eyes that are not held in place with plaster, and have no easy access inside the head, adding balls of cotton to the open eyes and wrapping them in place with tissue or cloth can help keep them from shaking loose or scraping off the lashes.
Wrap doll with cloth or tissue protecting any parts that could rub together during shipping with a layer or two of padding. THEN do the bubble wrap. Tape the bubble mummy style... helps prevent shaking and shifting of the body. Make certain nothing rattles or shifts in the box. Tape two or more bubble wrapped items together so they can't possibly strike one another during travel. Fill the voids with anything and have a inch or two of fill between the packed items and the box walls.