My mother has dementia, alzheimers, diabetes, arthritis, neuropathy and heart disease. I take care of her full time. Getting help for the bath tub would give her some independence back. I have to help her put her legs in the tub. I stand by her in case she gets unstable and she doesn't mind but always says she wants to be independent.
It appeared my relatives would need a whole bathroom remodel but the OT had great solutions that could be done quickly for much lower cost.
There can be compromises too. Eg a basin & flannel wash while seated in the bathroom could be done independently - while a shower/wash with handheld hose could be with your assistance. Could alternate days.
Even just a simple thing like having a chair to sit on while drying & dressing can improve safety. (eg slips / trips on pant legs).
From the ailments you mentioned, I would be thinking high falls risk due to any one of them: stiffness (arthritis), lack of sensation (nephropathy) fatigue (heart disease) & most importantly, possible lack of insight (dementia). The sum together = very high Falls risk (my opinion only based on words, not seeing your Mother obviously).
Sometimes an elder is happier to change routine if "that nice OT man/lady said I should do it this way now" 😉