I don't know about diaper rash specifically, but bubble bath can cause all kinds of skin reactions and also vaginal infections in little girls. I stopped using it with my stepdaughters, since both were prone to childhood eczema, and it was an irritant. Often it has pretty powerful ingredients! If you're going to use it, I would say to at least get the one with the least additives you can, and fully rinse your daughter afterwards in clean water so it doesn't coat her skin. But given what her reaction may have been, I'd give it a rest for a while. (I love bubble baths, though!)
If she loves bubbles (and who doesn't?), why not stick to blowing them? 'Bubble juice' is a constant favourite here.