Mom has dementia. Bath 2-3 days/wk, new clothes 1+ day/wk, but sleeps 12-14 hours and is inactive. Might have UTI - most likely culprit?

Dementia and apathy. You don't say if this is new or ongoing. If new, it could be a uti. Never go wrong with checking. Also depression could cause these symptoms. As dementia progresses, people lose the ability to keep on top of self-care. At this point, it helps to have a caregiver prompt and assist her to do these things. Your local alzheimer's chapter will most likely have a support group for info/tips.
Get it checked out. Uti's are really simple to check and rule out. Take her to your doctor to see. If you are helping with care and notice cloudy urine and maybe some additional confusion, not just memory issues, i'd say you were on the right track. A simple course of antibiotics helps clear a UTI rather quickly.