Aiming at decreasing average passenger wait time at stops, headway adherence is used to measure the route-level service reliability for high frequency bus route services. Considering the fluctuation of passenger demand and the stochastic nature of running time on road segments, a fixed route of high-frequency bus services was set to be a case study. In this case, Monte-Carlo method was used to simulate the process of bus services on this route. Headway variation and average passenger wait time at stops were statistically calculated for two different situations with bus overtaking or no-overtaking in the case of bus bunching. The results show that, under both situations, the accumulative headway variation tends to become bigger, which results in worsening service reliability at stops downstream. However, allowing the following bus to overtake the previous bus would result in better service reliability and smaller passenger wait time than not allowing bus to overtake.