Trying to be sagelike and failing miserably!
You probably already know this but her anger means she loves you, oh so much.
I know its little comfort but I've noticed that people with Alzheimers can be the meanest to the ones they love the most. Its the people we love unfortunately that we take out all our emotions on. Its the people who mean something to us that can affect us. Think of divorce for example, the only nice divorce is when the two people in it no longer really care about each other and are happy to go their own separate ways, or they still really love each other, know each other and don't offend each other and come to an agreement. Divorces get messy because usually one or both still care about each other in some way but the other has changed, and so they get hurt by the other's behaviours or actions and so lash out. So too with dementia, the person you love becomes someone other than the person you thought you knew. In the case of the sufferer, they have to deal with the realisation that they are no longer the person you loved. This must be very scarey for them. Perhaps they are scared that we will stop loving them, I know I've been very mean to past loves when I thought they might stop loving me because I wasn't the person they initially thought I was. Its a self-protection thing I think.
For people with dementia, the rest of the world seems to fade, they no longer seem to care about what strangers think of them, they care about what the people they love think about them. I know if my loved one told me I needed a bath, I'd probably lash out at them due to the embarassment, no matter whether what they said was true. And when you have only half of your faculties undamaged it is very difficult to control these emotions as a normal rational adult would, and behave tactfully, or even make peace afterwards.
You've probably already reasoned all this out in your head and now I feel immense pressure to say something absolutely brilliant because of 1234's wonderful comments. But I am at a loss for I know that no matter how logical it all is in your head, it still hurts. And it hurts to hurt them. I have no sagelike advice on solving the bath problem either, we are blessed here in Australia with warm weather so although that means more sweat and more smell, swimming and standing in the monsoon like rain can be an easy solution! At one stage though we did resort to partial wet washer baths when Dad was asleep, only doing as much as we could until he woke, and then look innocently at him, when he opened his eyes!!
Sorry I couldn't be of much help.