That shouldn't be because of a UTI. Does she complain of pain during urination? However, that doesn't mean other parts down there couldn't be irritated. Does she seem overly red in that area? When my daughter was that age she developed a reaction to the materials in her diaper and because she was irritated down there the bath didn't feel very good. My naturopath had me put baking soda and apple cider vinegar in the bath. I wasn't sure about it, but I admit that the vinegar (it MUST be apple cider vinegar and preferably with the Mother still in it) really is soothing. If she has a yeast infection (yes, it really can happen on little girls) it really helps with that. Just simply fill the tub to the top of her hips or belly button, and place a half cup of vinegar in; that's it. There will be a slight smell but it will dissipate. Let her sit in it as long as she'll stand it. That works for adults too! (Especially if you have chronic yeast infections, it helps balance the PH). Also, avoid all bubble baths and soaps/body wash with a lot of additives and chemicals in them. They're not nice to such delicate skin.
It's also possible that something inadvertently scared her and she's connected it with the bath, hence she doesn't want one. Have you tried giving her a bath in a different location such as the kitchen sink or a large plastic tub on the table? If she's fine with that, then it's something to do with the bath tub. If it doesn't help, it's probably the water scaring her and with a lot of love and patience, she'll get over it. Good luck!