I just relearned how to ride a bike. (I had it down as a kid but my mother thought it was too dangerous yada yada.) I had tried in my mid-twenties and again last summer when I was almost 51 but it didn't click until about 2 1/2 weeks ago. What motivated me to stick with it enough to kind of get it? I had to have a bike that I loved and that was small enough I felt comfortable about falling off of it. In my case, that was an Avigo Knockout which is a very pink 18" BMX bike. A lot of women start out on bikes that are too large for them. Guys seem to be fine with riding a bike that barely allows them to touch the balls of their feet to the ground but women I know- especially in my age group and older- prefer to be able to stand flat-footed. That might mean a 20" bike or a 24" or a 26" with a smaller frame and the seat slammed all the way down but unless she feels safe and the process is approached with patience on all sides, there's no chance of her moving up to something she can ride alongside you on because she won't be on a bike at all.
The other big factor was not wanting to be left behind or, as I put it, part of a mixed relationship between someone who rides and someone who doesn't. (It really helped that I'm a volunteer mechanic in a not for profit shop and saw plenty of happy couples and women who had learned or relearned to ride at an ahem advanced age.) He rides everywhere all the time and has ridden for years so it would be quite a while- if ever- before I could keep up with him if he went all out. Luckily, he has no problem riding in circles or going very damned slow while I'm learning and becoming more comfortable.
I moved up from the 18" BMX bike to a Trek 830 with 26" wheels and a 16 1/2" frame. A mountain bike is great because I love climbing- so far- and it makes me feel strong and powerful to be able to ride on uneven surfaces. I still am not comfortable going very fast downhill and the other day I realized it's because I'm worried about losing control of the bike and being injured and having no way to pay the resulting medical bills. So I'll be riding the brake a lot until January 1st but I'm out there and, more importantly, *we're* out there together.