Unlike squared (or alike) quadrotors, elongated bi-copters leverage natural superiority in crossing tight spaces. To date, extensive works have focused on the design, modeling, and control of bi-copters. Besides, a proper motion planner utilizing bi-copters' shape characteristics is essential to efficiently and safely traverse tight spaces, yet it has rarely been studied. Current motion planning methods will significantly compromise their ability to traverse narrow spaces if the map is inflated based on the long dimension of the bi-copter. In this paper, we propose an efficient motion planning method that enables the safe navigation of bi-copters through narrow spaces. We first adapt a dynamic, feasible path-finding algorithm with whole-body collision checks to generate a collision-free path. Subsequently, we jointly optimize the position and rotation of the bi-copter to produce a trajectory that is safe, dynamically feasible, and smooth. Extensive simulations and real-world experiments have been conducted to verify the reliability and robustness of the proposed method.