Have you had any discussions with your vet about getting a hygiene clip for your rabbit? That can be helpful when a rabbit has a chronic dirty bottom. Is it possible that your rabbit is in pain due to the limp? If so, low doses of a pain reliever, such as Metacam might help her be more limber and more able to keep clean. Sometimes butt baths are necessary, but it would be good if you could address the problem with a hygiene clip and/or some pain meds if warranted, so that you don’t have to bath her so often.
Instead of using some kind of rabbit shampoo when you give butt baths, you could try a small piece of a bar soap, such as Kirk’s Castille. It is hypoallergenic, contains no animal products, is not tested on animals and it comes in an unscented version. I use that soap for myself. I also use Clearly Natural or Clearly Magic glycerin soap, which like Kirk’s, is hypoallergenic, no animal products or testing, and comes in unscented. I have used small pieces of that soap in the water when I had to give a few butt baths to one of my elderly past rabbits who was unable to keep clean.