It is simple. A bike will be stable without a rider because if it tilts to the left, the front wheel will also tilt to the left (as the hinge is behind the center of gravity). This results in a left turn, and the centrifugal force of the turn will bring the bike back upright and straighten the wheel.
The rider turns the bike by moving the handle bars slightly in the opposite direction he wants to turn. Then the bike falls in the direction he wants to turn, and the handle bars are then rotated in that direction. To straighten out, the handle bars turn a little tighter, and the centrifugal force of the turn pushes the bike back upright.
The rider turns the bike by moving the handle bars slightly in the opposite direction he wants to turn. Then the bike falls in the direction he wants to turn, and the handle bars are then rotated in that direction. To straighten out, the handle bars turn a little tighter, and the centrifugal force of the turn pushes the bike back upright.