Mother with Alz takes long baths, but does not wash. Any suggestions for a good hygiene wash to add to water?

She needs help washing.
Just as she bathed you when you did not know how to properly bathe you now must do the same.
This also goes for other ADL's (activities of daily living) toileting, brushing her teeth, washing her hands and it will progress (regress?) to eating with fork, spoon to fingers, then from "regular food" to minced, then pureed.

Someone needs to help her with washing, either her family caregiver or a hired aide. Perhaps start getting everyone used to the idea by being on hand "to make sure she can get in and out safely" and staying to help wash her back, from there you can hand her a wash cloth and prompt her to wash herself, or gradually take that on too. I agree with JoAnn that long soaks and soaps and chemicals are probably not a good idea.

Now just my opinion, I don't think bathing is a good thing especially for long periods. When my daughter had a series of UTIs the first thing I was asked did she take bubbles baths frequently. Answer was yes. Seems because of girls short urethras soap get in there and breeds bacteria. Once we stopped the bubble baths, switch to cotton briefs and went back to white toilet paper (colors were in then) no more UTIs.

All I can suggest is body wash using a puff and you wash her down. If you don't have one, get a handheld shower head to rinse her off well especially in that area.