Autonomous vehicles have already been introduced on city roads, and they are poised to become a significant component of the transportation system. Buses, being a critical part of public transport, are particularly suitable for the advancement of higher levels of autonomous driving technology due to their fixed routes and scheduled times. This paper investigates the stopping behavior of autonomous buses on future urban roads under mixed traffic conditions. Specifically, it examines the lane-changing and following behavior of autonomous buses when entering and exiting stops. The study proposes a game theory-based control strategy for bus entry and exit, modeling and simulating driving decisions using game theory principles. The model is solved and simulation is conducted to verify the feasibility and advantages of the proposed strategy. This strategy can provide enhanced decision support for the control of autonomous buses in mixed traffic flow.