Understanding human/bicycle interactions is crucial not only for enhancing bicycle (motorcycle) safety but also for designing new bicycle-based rehabilitation devices. In this paper, we present stability analysis of a human neurological control of stationary bicycles. The stability results are obtained through using the sweeping frequency method and the stability charts for time-delay dynamical systems. The results show that through only human rider's upper body movement, it is impossible to stabilize the stationary bicycle; however, with additional bicycle steering control, the riders can balance the bicycle under three delays in the neurological system. We present and illustrate these stability conditions for the systems with a set of model parameters of typical healthy riders.