I wonder if you have a Parkinson's nurse who can advise you?
Or you could ring the helpline who could put you in touch with a Parkinson's welfare officer.
You need an assessment and info on social services help available...there may be a grant to put a wet room in the downstairs area...with a shower stool it is very convenient.
Some care homes offer facilities for bathing people who still live at home.
I don't enough about the help available but lots of people do!