We use plain glycerin soap. No dyes, no scents, pure. I get it at Whole Foods, it's the 365 (store) brand. I have extremely sensitive skin and it's the only stuff I can use. It's great for our daughter too. I made the switch this winter after using things like Dove Sensitive, etc., and I usually have to lather on the lotion during the winter. This winter though, since I've been using the 365 soap, I haven't had to use lotion at all! It's really improved my skin, and it's so gentle.
If her skin needs to stay moisturized, you're probably better off not even using soap, and if you do, use something like a plain glycerin soap. You can wash just using warm water and a washcloth. Maybe even add a little baking soda to her bath water to help sooth the bumps?