Try her out on a Bike E, a sort of semi-recumbent. I rented one for a few days last year and enjoyed it. Lots of models available, and I think some are in her price range. Get her to ride it, not just look at it and say "Yuck."
If that doesn't work, how about an Electra Townie or another bike with that kind of frame, "Pedals forward" or whatever it's called. A friend of mine, a 30-year cyclist who's done dozens of centuries, rides one around town and really likes it. The seat is a little behind the crank and low, so she can get both feet on the ground easily but still have full leg extension.