Hi ntf, I am new to this forum but your question caught my attention. Maybe you have said before how advanced your mother's dementia has become, but as it progresses some really oddball issues come up that really do make sense but just don't come to mind for most.
Cindy and Claudia have good tips, timing, safety, making it a 'spa' treatment, but both take it for granted that you assist your mother with her bath rather than are just asking her, (begging her) to please shower. Does she take care of herself in the bathroom?
First, daily showers are not usually necessary and can dry out their delicate skin even with lotions. Daily (and more if she is incontinent) cleanup of her personal areas is another matter, because of odors, irritations and infections.
What you need to consider is why she resists, and to what degree (does she get frantic or just brush you off).... Does she say she's too tired, afraid of falling, cold or embarressed, or do you ask her to and she forgets you asked (or forgets she hasn't yet.),
They may not recognise the reflection in the mirror and be nervous about getting naked (hang a towel over the mirror at shower time). Pre warm some towels for her in the dryer and wrap them in a light blanket to keep them warm so she doesn't get that sudden chill of a wet person coming out from under the warm water. Definetely use a bath seat for her if you aren't already and put a hand towel on it for her to sit on, I doubt anyone likes the feel of plastic on a bare bottom. Install a grab bar (safety bar, whatever you call it) if it hasn't been done.
If you haven't been assisting her, it may be time to start. Pick a time that doesn't interfere with her meals, naps, and favorite TV (and hopefully yours). If she likes "Gunsmoke" tell her it is time to get ready for her date with Matt Dillon, My mother's date is with Andy Griffith, get the idea. Have everything ready and tell her it is time to clean up and with as little fuss as possible escort her to the shower and begin. It may help to give her a choice (no, don't ever ask when she wants her shower , ask only questions with A or B answers) Would she like to put on her pink PJs or the Blue ones when she gets out? Does she want the Jasmine or the Lavender lotion? Choose a question with an answer that makes the shower a done deal .
It takes practice and a little planning to pull this off, so if at first you don't succeed, try again. It may help to practice on less stressful issues before trying it with the shower to get your technique down and build your confidence.
Good luck