Understanding how human balance and control bicycles is helpful for not only designing bicycle-based rehabilitation devices but also studying physical human-machine interactions. We present stability analysis of a rider-bicycle system under the rider's steering and upper-body movement balancing controls. The dynamic model of rider-bicycle system is first constructed to integrate the rider's upper-body movement with the moving platform. We then present a human balance control strategy based on the human riding experiments. The closed-loop system stability is analyzed and discussed. Quantitative influences of the bicycle physical parameters, human control gains and human control time delays are also demonstrated and discussed.