For a biped pole-climbing robot (BiPCR) with dual grippers to climb poles, trusses or trees, a feasible collision-free climbing path is inevitable. In this paper, we utilize the sampling-based algorithm, Bi-RRT, to plan a feasible single-step collision-free climbing motion for BiPCRs in spatial trusses. Under the orientation limit of a 5-DoFs BiPCR, a new state representation along with corresponding operations including sampling, metric calculation and interpolation is presented. A simple but effective model of BiPCRs in trusses is proposed, through which the climbing path planning problem is transformed to be similar to that of an industrial robot. In addition, the pre- and post- processes are introduced not only to expedite the convergence of the Bi-RRT, but also to ensure the safe movement for the robot near the poles. The effectiveness and efficiency of the presented Bi-RRT algorithms for climbing motion planning are verified in the simulation.