We focus on the problem of efficient anytime kinodynamic planning for systems with complex dynamics in unstructured environments that make using precomputed motion primitives infeasible. Directly applying A* here is computationally infeasible due to the curse of dimensionality. Methods such as Hybrid A* (HA*) address this by pruning the search tree by discretizing the state space, but the coupling between pruning and discretization resolution can eliminate a vertex on the solution path. The Incremental Generalized Hybrid A* (IGHA*) breaks this coupling by organizing anytime search over a hierarchy of resolutions and by freezing vertices for later expansion rather than pruning. However, IGHA* can still freeze a vertex on the solution path, forcing the search to spend expansions elsewhere before reaching it. Our key insight is that bidirectional-IGHA* (Bi-IGHA*) not only gains the expected reduction in effective search depth from classical bidirectionality, but also mitigates this frozen-vertex barrier: when one search is blocked, the opposing search can reach it at a low resolution. We formalize this structural separation between Bi-IGHA* and IGHA* and empirically show a reduction in effective branching factor beyond the theoretical expectation from classic bidirectionality alone. Through open- loop experiments in R3, R4, and R6, we show that Bi- IGHA* substantially reduces expansions over IGHA*. Closed- loop experiments further demonstrate improved performance and feasibility in simulation and on a real-world robotic system. Link to Website: https://personalrobotics.github.io/IGHAStar/biighastar.html

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