With the technological advancements, the autonomous vehicle (AV) is expected to play an active role in the future transportation system. An AV-based public transportation system was recently proposed to unleash the full capability of AVs to provide effective and flexible transportation services. It establishes a new public transportation market which can accommodate multiple vehicle operators. Such multi-tenant system encourages market competition for better quality of service. The pricing process in the original proposal was designed based on the Vickrey-Clarke-Groves mechanism, but it is vulnerable to the problems of payoff reduction and shill-bidding. In this paper, we re-investigate the pricing process to address these vulnerabilities. We formulate it as core-selecting reverse combinatorial auctions and investigate the properties of the ``core''. We establish a core-selecting mechanism which can maximize customer's utility and prevent shill-bidding. We analyze the theoretical properties of the formulated auctions and the core-selecting mechanism. We verify the results with extensive simulations. The simulation results show that the core-selecting mechanism can result in lower service charge, and suppress untruthfulness, shill-bidding, and coalition formation. It can produce auction results in linear computation time, making it scalable and practical.