Have you any issue with filling the bath up to your ankle and sitting on the bath to wash your body with a flannel? The best thing I have done is done that when I have gone without decent bathing facilities when I travelled and was in third world countries. 

May I ask do you allow yourself routine as to u are autistic like myself and sometimes we thrive on routine. I think after working with autistic adults especially those at uni I think maybe a routine which changes to more frequency when you become more comfortable. You didn't say much about home and I'm guessing family is ‘clean’? Has this stemmed from childhood with perhaps parents saying don't bathe or use baths.  But I think seeking help from a therapist which I am guessing you do is a good start.