How do I introduce the idea of Assisted Living to my 96-year-old mother?

What you also might do is look a respire week at a "tiered" facility - ones that go from IL, AL to NH & hospice that also have a rehab unit or floor. At 96 you don't want to go thorough a whole new move a second time.

She may need placement in community based LTC within a NH. It still will be considered skilled nursing but won't be quite as much $$ as a highly skilled nursing would be. It's all expensive but one would be $ 4K a mo and the other $ 7 - 8K a month. Huge difference.

Personally I would do a 1 week respite care because if the place isn't a good "fit" for her you will need to do another 1 week try out at another place.

As Lili said, the mobility issue will be a big factor in all this.

If she is no longer a candidate for day care she may not be able to function at an ALF. Their services are minimal. They usually include meals (they have to get to the dining area), housekeeping, transportation to appts., and activities. Personal care is usually extra. The best thing to do is to make appts. and go by yourself at first. Come armed with a list of questions based on your mother's needs. Remember that the first people you meet are sales people. They will promise you everything - ask if they will put it in writing. Your biggest challenge may be her mobility issues and getting medical care. Some places have in-house nursing and doctors...most don't. She may need another setting such as a nursing home or a hybrid of an ALF and NH especially if she has dementia. Ask if they have a memory care wing.
One other thing to consider is an ALF setting and hiring addtional care to meet her needs.
Without knowing more about her mobility and health issues it is hard to say which would work best for her.