Sadly she doesn't get over her anxieties nearly as fast as she forms them, slowly slowly on that front.
It is hard to watch them suffer from anxiety, especially at such a young age. My DS (almost 3) makes quick decisions about what scares him and then, too, will hold on to that fear with both hands for a very long time. Yesterday, he sat on his tricycle for the first time ever (he got it when he was 18 months). He would not pedal, but he allowed me to push him around. And he even let me put his helmet on (another big fear). Small little victories like that mean so much more when we know how hard it is for our little ones to work through it. Best of luck to you with the bath fear. Have you tried asking her for suggestions about what would make it less scary? I find this helpful now that DS is articulate. And he actually comes up with some pretty unique ideas!