The efficiency of sampling-based motion planning brings wide application in autonomous mobile robots. The conventional rapidly exploring random tree (RRT) algorithm and its variants have gained significant successes, but there are still challenges for the optimal motion planning of mobile robots in dynamic environments. In this paper, based on Bidirectional RRT and the use of an assisting metric (AM), we propose a novel motion planning algorithm, namely Bi-AM-RRT*. Different from the existing RRT-based methods, the AM is introduced in this paper to optimize the performance of robot motion planning in dynamic environments with obstacles. On this basis, the bidirectional search sampling strategy is employed to reduce the search time. Further, we present a new rewiring method to shorten path lengths. The effectiveness and efficiency of the proposed Bi-AM-RRT* are proved through comparative experiments in different environments. Experimental results show that the Bi-AM-RRT* algorithm can achieve better performance in terms of path length and search time, and always finds near-optimal paths with the shortest search time when the diffusion metric is used as the AM.