Hey, I just went through this with my daughter.
She had a trike and then a 12" wheeled bicycle with training wheels. The problem with training wheels is that kids tend to lean to the outside of a corner to turn with training wheels. Of course, this is opposite to riding without. It's really confusing to them, and that's why they fall so much.
Anyway, I took the training wheels off her little bike, but I also took the cranks, pedals and chain off. The bottom bracket was just a hole. I lowered the seat a little and just let her use it like one of those striders. I went out with her several times so she could get the hang of it. I always kept it real low-key...just going out and playing at the park or something. We did this for a couple weeks.
Last Saturday I put the cranks, chain and pedals back on the bike, but no training wheels. Then I told her to coast down our driveway like she had been before. Which she did. Then I asked her to do it again. This time, on the way down, she put her feet on the pedals and rode right by me. Damnedest thing you've ever seen. We've gone out twice since then, and she is riding like a champ. She never had to go through the hours of falling over. She's definitely got a proud papa.