Maybe you could wash her hair separetely, like say at the kitchen faucet? Then maybe for a while a "bath" could be just her standing in the tub, (no water in it) you wash her body and rinse her by pouring water over her body. Maybe if you did that for a couple of weeks, and then slowly work your way up? Like one day while she is standing, run the water, then when she's ok with that, you can try to get her to sit. Mayne bring bubbles into the bathroom, and tell her "We can only use tubby-bubbles if we sit down." I'm all about taking things slow!
BT..my dd went through this...I never did figure out why she got so suddenly scared, but it stopped after about 2 weeks.