I think it's the steering that keeps you up. When riding, gradualy slow down till you stop. At the moment you come to a complete stop you will start steering like crazy in an attempt to keep balance. Ride in the snow an you'll see that it's impossible to make a straight track. You are constantly steering the bike.
When you get down to it, it's merely complete Zen mastering of bicycle balance. If you had to conciously think about the necessary amount of handle bar angular rotation to correct balance, you could not do it.