Interaction intention anticipation aims to predict future hand trajectories and interaction hotspots jointly. Existing research often treated trajectory forecasting and interaction hotspots prediction as separate tasks or solely considered the impact of trajectories on interaction hotspots, which led to the accumulation of prediction errors over time. However, a deeper inherent connection exists between hand trajectories and interaction hotspots, which allows for continuous mutual correction between them. Building upon this relationship, a novel Bidirectional pOgressive Transformer (BOT), which introduces a bidirectional progressive mechanism into the anticipation of interaction intention is established. Initially,(BOT) maximizes the utilization of spatial information from the last observation frame through the Spatial-Temporal Reconstruction Module, mitigating conflicts arising from changes of view in the first-person videos. Subsequently, based on two independent prediction branches, a Bidirectional Progressive Enhancement Module is introduced to mutually improve the prediction of hand trajectories and interaction hotspots over time to minimize error accumulation. Finally, acknowledging the intrinsic randomness in human natural behavior, we employ a Trajectory Stochastic Unit and a C-VAE to introduce appropriate uncertainty to trajectories and interaction hotspots, respectively. Our method achieves state-of-the-art results on three benchmark datasets Epic-Kitchens-100, EGO4D, and EGTEA Gaze+, demonstrating superior in complex scenarios.