Autonomous landing on mobile platforms is crucial for extending quadcopter operational flexibility, yet conventional methods are often too inefficient for highly dynamic scenarios. The core limitation lies in the prevalent ``track-then-descend'' paradigm, which treats the platform as a passive target and forces the quadcopter to perform complex, sequential maneuvers. This paper challenges that paradigm by introducing a bi-directional cooperative landing framework that redefines the roles of the vehicle and the platform. The essential innovation is transforming the problem from a single-agent tracking challenge into a coupled system optimization. Our key insight is that the mobile platform is not merely a target, but an active agent in the landing process. It proactively tilts its surface to create an optimal, stable terminal attitude for the approaching quadcopter. This active cooperation fundamentally breaks the sequential model by parallelizing the alignment and descent phases. Concurrently, the quadcopter's planning pipeline focuses on generating a time-optimal and dynamically feasible trajectory that minimizes energy consumption. This bi-directional coordination allows the system to execute the recovery in an agile manner, characterized by aggressive trajectory tracking and rapid state synchronization within transient windows. The framework's effectiveness, validated in dynamic scenarios, significantly improves the efficiency, precision, and robustness of autonomous quadrotor recovery in complex and time-constrained missions.