Private room as long as possible or shared room from the start?

Definitely private room. My mil with Dementia was in a shared room in a Nursing Home and was constantly rummaging through her roommates personal belongings. Also she constantly asked her roommates why they were in her room. After several room transfers she was finally assigned a private room.

Private, I cannot imagine living with a stranger in an AL room. Even if Mom goes on Medicaid, she may be able to stay in her room.

My worst fear (if you want to call it that) is having to share a room with a stranger for any length of time. I am a friendly person but I am used to my privacy. I have visited people in homes and rehab and have seen a lot of entitled roommates. With DHs Aunt, her roommate did not like TV so had none. She also didn't like Aunt using hers. So the maintenance man hooked up a headset so Aunt could use the TV. Then the roommate didn't like that the TV was even on.

PRIVATE as long as possible.

This is definitely a decision to make with your Mom if you are able. She may be like my brother and opt for alone as long as she is able. Or she may be more a social type who would like at least to TRY to have a roommate. You are the best judge of what Mom may like in this instance. It is a pure choice that has no better or worse except that dependent on Mom's lifestyle. Surely do wish you both the best.

Me, I would opt for a private room, I have two in homes, one AL (age 97) another in MC (age 84), neither would at this point would do well in a shared room.

There are too many personalities to deal with when a small space is shared.

I will cross that bridge later, if I need to, for now, I want them to have their own get away space.