Routing design is an important aspect in aiding the completion of the Quantum Processing Unit (QPU) layout design for large-scale superconducting quantum processors. One of the research focuses is how to generate reliable routing schemes within a short time. In this study, we propose a superconducting quantum processor auto-routing method for supporting scalable architecture, which is mainly implemented through the bidirectional A star algorithm, the backtracking algorithm, and the greedy strategy. By using this method, the number of crossovers and corners can be reduced while efficiently completing the processor routing. To verify the effectiveness of our method, we selected 5 types of qubit numbers for processor routing experiments. The experimental results show that compared to the improved A star algorithm of Qiskit Metal, our method reduces the average execution time by at least 43.61% and 41.68% in serial and parallel, respectively. Compared with four other routing algorithms, our method has a minimum average reduction of 10.63% and 1.21% in the number of crossovers and corners, respectively. In addition, our method supports the processor routing design of planar and flip-chip architectures, and can automatically process both airbridge and insulation types of crossovers. Therefore, our method can provide efficient and reliable automated routing design to assist the development of large-scale superconducting quantum processors.