She sounds very tactile defensive. Often a tactile desensitize program will help with this. If you haven't already, find a good private OT who has good ideas on how to help with tactile defensiveness. For example, my son did not like to be touched when he was young. So we did a brushing program with a special brush. Problem solved. A good OT should have lots of ideas on this problem.

My daughter loves plushie's we pick out 10 and line them up on the sink unit and they watch her..we use glow sticks and lights out in the tub is a fav..Good luck keep trying .

Shaving cream they can draw and make things with it

Maybe you could try a baby steps approach? Tell her at a time that is not bathtime that she can do tub play. Dont make her get in the tub, just sit beside and play with some toys that are floating in the water. See if you could get her interested (or at least ok with) putting her hands in, then an arm then both feet and see if you can desensitize her? This would probably take a few weeks of consistent work but could be worth a shot.
Also - you've probably already tried this but have you tried putting more (or less) water in the tub? I can see it being uncomfortable if she just has a few inches of water because her whole top half would be wet and cold. Or maybe she would do better with less water? It doesn't take that much to get clean.
Good luck!

stuffed toys ...my girl likes TY beanie babies.::))))