Katy, I'd like to recommend a technique that can be used to teach anyone to ride a bike at any age. It's not at all scary and it helps you get confident with balance and steering before you have to put your feet on the pedals. I've seen a video but can't find it right now, but here's a detailed description of the method: http://ask.metafilter.com/14303/Like-Learn…
I agree with some of the commenters that this technique is improved by removing the pedals entirely at first so your legs can swing as you walk/ride the bike.
Another person who didn't learn until adulthood actually exists in Portland? I'm 19, and I learned in March. Like ballet, my bike-learning was stopped with a tantrum and I just never really picked it back up. As one with no car, I was left with getting around on the bus, and my mother was always asking me when I would join the other "unwashed youths" of the city in biking everywhere. And then I started dating a bike commuter, and moved out of my campus apartment and onto Hawthorne, and I pretty much had no choice but to learn how to ride a bike. I learned the good old-fashioned way, having someone (my boyfriend) hold me up and walk/run with me, which helps because the hardest part is starting from rest. Definitely put your seat a little shorter than is ideal for efficiency, so you can easily put your foot down.
I agree with some of the commenters that this technique is improved by removing the pedals entirely at first so your legs can swing as you walk/ride the bike.