Find out if it's because she's worried about getting sucked down the drainhole - I remember being terrified at one stage of that very early on.

Or maybe she had an ouchy experience - like shampoo going in her eyes or pulling scalp if you were shampooing her hair - and that's put her off?

Also (cos I'm assuming it's your youngest DD we're talking about) maybe her depth perception is kicking and she's now aware the water seems 'deep'?

SUGGESTIONS
Put a rubbery mat in the bottom so it's not slidey & she can see the bottom
Add bubbles or food dye - provide a 'fun' distraction
Use a hand held shower tube (you know, the rubber ones that fit over the tap) and sit her in the bath (with the plug out) and wash her that way
Hop into the bath yourself and sit her on your lap (so she feels secure)
Take her thru the shower with you.
Put a toy over the drain hole when you're letting the water out so it drains out slower and doesn't make a loud scary noise.

Re the hair - perhaps it's a good idea to have a hairdresser cut the matted parts out (instead of shaving!) and try again but use conditioner & a wide comb *every* time you wash her hair.