The Autonomous Vehicle (AV) is expected to be an important "building block" of the future smart city. Recently, an AV-based public transportation system has been successfully developed to provide precise, effective, and intelligent public transportation services. For better quality of service, the system encourages market competition by accommodating multiple AV operators. To facilitate the pricing process, a pricing mechanism was developed but it can only process one service request each time. This can significantly impair the overall passenger admissibility, especially when there are many outstanding requests to be processed. In this paper, we re-design the pricing mechanism for handling multiple requests simultaneously. To do this, we formulate the key component of the mechanism, i.e., request-AV allocation, as a double combinatorial auction-based process. We construct a new winner determination problem that can accommodate requests of different AV service types. We also investigate its duality to devise an efficient service charge determination rule. We evaluate the performance of the proposed mechanism and charging rule with extensive simulations. The results show that the mechanism can result in better social welfare than the original scheme. Moreover, we examine the computational time required and the percentage of successfully served passengers. The simulations demonstrate that the mechanism can make the AV public transportation system more practical.