Transit Signal Priority (TSP) is a system designed to grant right-of-way to buses, yet it can lead to delays for private vehicles. With the rapid advancement of network technology, self-driving buses have the capability to efficiently acquire road information and optimize the coordination between vehicle arrival and signal timing. However, the complexity of arterial intersections poses challenges for conventional algorithms and models in adapting to real-time signal priority. In this paper, a novel real-time signal-priority optimization method is proposed for self-driving buses based on the CACC model and the powerful deep Q-network (DQN) algorithm. The proposed method leverages the DQN algorithm to facilitate rapid data collection, analysis, and feedback in self-driving scenarios. Based on the arrival states of both the bus and private vehicles, appropriate actions are chosen to adjust the current-phase green time or switch to the next phase while calculating the duration of the green light. In order to optimize traffic balance, the reward function incorporates an equalization reward term. Through simulation analysis using the SUMO framework with self-driving buses in Zhengzhou, the results demonstrate that the DQN-controlled self-driving TSP optimization method reduces intersection delay by 27.77% and 30.55% compared to scenarios without TSP and with traditional active transit signal priority (ATSP), respectively. Furthermore, the queue length is reduced by 33.41% and 38.21% compared to scenarios without TSP and with traditional ATSP, respectively. These findings highlight the superior control effectiveness of the proposed method, particularly during peak hours and in high-traffic volume scenarios.