My daughter had extremely sensitive skin, and we stopped using body wash on her. If they are bathed pretty often, at that I young I do not see a point in using soap if you still clean everything well. We did use shampoo about every other time and just cleaned with water and a washcloth.
If you feel the need to use soap try to find the most extra sensitive kind you can. Some people might recommend using natural soaps however those can still irritate sensitive skin. Though the ingredients are natural they can still cause mild allergic reactions and still have an odor or can leave residue. The same with lotions.
Also consider if the baby is being completely rised off with fresh, clean water. Using a baby bathtub will not completely rinse soap off enough, because you are using water that already has soap in it.
We started taking her in the shower(when it was time for one of us to) when she was little. One of us would get in and hold her, while the other one stood outside the shower and reached in to wash her. Of course making sure the temp was ok and her head was out or covered properly. (if you point the shower head down a little straighter, rather than up and out over you, you will have much better control of where it gets on them) It just took a couple minutes and her skin was much healthier and noticably softer not irritated.
Just wanted to add that I second the baby oil of Grandma TM. We always use it, especially in the winters she gets eczima, after her bath(now 4) it has never irritated her skin like most lotions.