In this paper, we address the vehicle scheduling problem for improving passenger safety in bus rapid transit systems. Our focus is on passengers waiting at street stops to enter terminal stations. To enhance their safety, we minimize deviations from the proposed timetable, thereby minimizing passengers' initial waiting time. We formulate an optimization problem considering the position, speed deviation, and passenger count at each stop, solved using dynamic programming. Numerical simulations validate the effectiveness of our approach in enhancing passenger safety. Our work is the first attempt to minimize waiting time for improved safety and the first to utilize position tracking for departure time matching.