Please don't despair - it really IS a phase. My daughter is now 8 but from the age of 2 right through until the age of 4 she was petrified of the bath, and I couldn't pinpoint what had set it off, either.
Some things to try:
Use one of those shower attachments that attaches to the taps, make it seem like something special, and wash her with that.
Put her favourite doll or plastic toy in the bath (one that she wouldn't usually have in the bath, or if you can, buy her something new).
Not sure if you already do this, but if not get her one of those visor thingies to shield her face from the water when washing her hair.
Do make it seem as if you're not at all bothered if she makes a fuss and you have to get her out of the bath - if you get stressed it makes it worse.
Try having a bath together so you can hold her if she's frightened - to reassure her that everybody has baths.
Failing that - just put her in the bath, wash her as fast as possible despite the screaming, without getting stressed yourself, and eventually she will grow out of it.
And she WILL grow out of it. My daughter has only just started to not mind water on her face and as I said, she's 8! Her latest trick is putting the shower jets on her tongue because it tickles and makes her giggle! But in saying all that, my daughter is petrified of swimming pools!!
Hope this helps :)