We study the bus schedule in the shuttle bus transportation system controlled by speedup. The bus schedule is closely related to the dynamic motion of the bus. The motion of a shuttle bus depends on the inflow rate of passengers and the delayed speedup control. The delayed speedup control has an important effect on the dynamic motion of the bus. We present the delayed map model for the dynamics of the shuttle bus with the delayed speedup control. The bus motion changes from a stable state, through a periodic state, to a quasi-periodic state by the delayed speedup control. The return map of the tour time displays a smooth closed curve and the bus motion is quasi-periodic. The dynamic transition to the quasi-periodic motion changes greatly with the delay time. We clarify the effect of the delayed speedup control on the bus schedule.