Ensuring bus priority is to improve traffic sustainability at the signalized intersection. To achieve this, the Bus Priority Lane (BPL) is adopted to provide exclusive right-of-way for buses. However, the BPL is underutilization if the frequency of buses is low. To address this issue, many studies focus on improving the BPL’s utilization efficiency by intermittently allowing general vehicles to access it. However, these studies still have some shortcomings: i) bus priority cannot be guaranteed if general vehicles run on the BPL; ii) the traffic system lacks resilience, especially when the traffic demand is unbalanced. This paper proposes a dynamic right-of-way allocation on the BPL considering traffic system resilience. On the one hand, it ensures absolute bus priority by controlling Connected Automated Vehicles (CAVs) to not interfere with buses. On the other hand, it can improve traffic system resilience by allocating right-of-way for CAVs with heavy turning-movement demand. To validate the effectiveness, the proposed control strategy is evaluated against the non-control baseline. Sensitivity analysis is conducted under seven unbalanced traffic demand levels, four congestion levels, and five CAV Penetration Rates. The results show that the proposed control strategy can ensure absolute bus priority and improve traffic efficiency and traffic system resilience.