your best bet is to wrap the torso and legs first, about two layers of wrap
then put the arms down and put more bubblewrap around till the thickness is about the same as the head, then wrapp bubbledwrap all around the doll including the head.
if the wig is detachable, take it off, put it in a hair net - if you have one, or in a ziplock and have that in the box or just be careful that your dolls hair is laying properly as you roll it in bubble wrap.
lastly put a bit of bubble wrap, packing peanuts, or PLAIN WHITE PAPER (not newspaper or any paper that's been printed on or dyed) in the bottom of the box and lay the doll on that. then put an equal amount over top.
Make sure the box is sturdy and the doll fits well. You don't want to be forcing the doll into the box.