How do I go about choosing a Geriatrician doctor for my mother?

Thank you for your answer. Very helpful.

If you have a health science center (large multi bldg place that is affiliated with a medical school, allied health programs, graduate biomedical programs), I’d suggest that you get her into the geriatric private practice with the doctors within the HSC. They will probably do a initial screening with a geriatric nurse practitioner, get some baseline testing done and then she gets placed with whichever MD fits her needs best.

One advantage to this is that should her main MD go on vacation there are others BUT to me the biggest advantage is that all those other geriatric specialists that she may end up needing - neurologist, endocrinologist, psych., rheumatologist, etc - all will have some sort of affiliation with the HSC and she can easily get an referral and be seen. Plus all the records will be easily retrieved.
If the HSC is big, they will have a research & clinical trials arm as well. My mom went into a HSC system a few years b 4 her dementia became obviously apparent. It was great as she was able to participate in studies that enabled her docs to pretty much determine she had Lewy Body Dementia and got her on outreach & drugs geared for Lewy.

Look for one who emphasizes quality of life over quantity. There are far too many doctors out there who want to treat every single ailment regardless of how much it costs or how much agony it causes. A good geriatrician knows every one of his patients is likely going to die under his care, and that's OK as long as they don't die BECAUSE of his care.