Forget about a full shower. It's too traumatic for someone with dementia, and it's risky b/c of fall possibilities. Use the no rinse products; they're safer and your mother doesn't need to shiver by getting undressed.
There are a lot of questions similar to this; you can use the search function with "parent won't bathe" or something similar and you'll find other suggestions, including making the cleansing experience more pleasant with rewards afterward.
Have her doctor order bath aides to help her bath. Dry shampoo and sponge baths can be used in between a full regular bath. The elderly only need a full bath once or twice a week.
There are a lot of questions similar to this; you can use the search function with "parent won't bathe" or something similar and you'll find other suggestions, including making the cleansing experience more pleasant with rewards afterward.