This paper introduces Bidirectional Tight Informed Trees (BTIT*), an asymptotically optimal kinodynamic sampling-based motion planning algorithm that integrates an anytime bidirectional heuristic search (Bi-HS) and ensures the \emph{meet-in-the-middle} property (MMP) and optimality (MM-optimality). BTIT* is the first anytime MEET-style algorithm to utilize termination conditions that are efficient to evaluate and enable early termination \emph{on-the-fly} in batch-wise sampling-based motion planning. Experiments show that BTIT* achieves strongly faster time-to-first-solution and improved convergence than representative \emph{non-lazy} informed batch planners on two kinodynamic benchmarks: a 4D double-integrator model and a 10D linearized Quadrotor. The source code is available here.