In this work, we introduce BBoE, a bidirectional, kinodynamic, sampling-based motion planner that consistently and quickly finds low-cost solutions in environments with varying obstacle clutter. The algorithm combines exploration and exploitation while relying on precomputed robot state traversals, resulting in efficient convergence towards the goal. Our key contributions include: i) a strategy to navigate through obstacle-rich spaces by sorting and sequencing preprocessed forward propagations; and ii) BBoE, a robust bidirectional kinodynamic planner that utilizes this strategy to produce fast and feasible solutions. The proposed framework reduces planning time, diminishes solution cost and increases success rate in comparison to previous approaches.