You can't say you are ignorant if as you say, you have NO experience with bikes. And you are showing no signs of being ignorant, because you have asked about something of which you profess to know nothing about to further your knowledge.
The gyro idea is a good one! However, you've been beaten to the idea as they are used in off road bikes to keep stability over jerky, rough terrain. A video shows this effect. http://www.youtube.com/watch?v=PCLlZsiYEps. The gyro is fitted in the rear wheel where it gathers energy from it's forward rotation then stores that energy when you slow down as demonstrated in the video.
Road bikes are a different matter. They do not have a gyro. They maintain their balance through the laws of cycle dynamics. ( as to a lesser extent the off road bikes do.) http://en.wikipedia.org/wiki/Bicycle_dynamicsIf you wish to avoid horrible mathematic equations like me, then another video might help. http://www.youtube.com/watch?v=jM27f...eature=channel
Best thing to do of course is simply to buy one and have a real giggle learning to brake, turn in, then balance the throttle on the way out of corners and the satisfaction of getting it right
Hope this has helped!