As Bird’s Eye View (BEV) perception becomes crucial for autonomous driving, unmanned aerial vehicles (UAVs) leveraging their native top-down perspective and agile mobility are increasingly deployed to overcome the inherent occlusion and limited sensing range of traditional vehicle-mounted systems. However, enabling UAV-assisted BEV perception faces a computation-transmission dilemma: onboard BEV inference is impractical due to tight resource constraints, while offloading high-definition visual data to edge servers is bottlenecked by limited wireless bandwidth. In this paper, we present AUBP, an adaptive video offloading scheme for UAV-based BEV perception. First, AUBP introduces a spatio-semantic synergistic mechanism that combines edge-side spatial feedback from BEV inference with lightweight UAV-side semantic extraction to preserve BEV-critical information while reducing spatial redundancy. To dynamically coordinate this mechanism under time-varying wireless channels, we formulate the adaptive configuration process as a Markov Decision Process (MDP). Subsequently, a Dueling Deep Q-Network (Dueling DQN)-based decision-maker is constructed to solve this MDP, dynamically selecting optimal encoding parameters to achieve a balanced trade-off between transmission efficiency and perception quality. Experiments on the UAV dataset for BEV perception under dynamically fluctuating network conditions demonstrate that AUBP consistently surpasses representative baselines.