we had a gal here for a while (on TE, I mean) that taught oldsters to ride bikes.
What someone else said is correct, lower the seat of a bike. there are lots of entry level bikes around, you didn't mention how tall she is - that can be an issue too, finding a bike that fits almost HALF of women (as the average height of women is 64"! )
and so far as falling, the balance idea is also good because bones thin as women age, and falling is not a good idea. (and it hurts)

Good luck