Sufficient cross-task interaction is crucial for success in multi-task dense prediction. However, sufficient interaction often results in high computational complexity, forcing existing methods to face the trade-off between interaction completeness and computational efficiency. To address this limitation, this work proposes a Bidirectional Interaction Mamba (BIM), which incorporates novel scan mechanisms to adapt the Mamba modeling approach for multi-task dense prediction. On the one hand, we introduce a novel Bidirectional Interaction Scan (BI-Scan) mechanism, which constructs task-specific representations as bidirectional sequences during interaction. By integrating task-first and position-first scan modes within a unified linear complexity architecture, BI-Scan efficiently preserves critical cross-task information. On the other hand, we employ a Multi-Scale Scan~(MS-Scan) mechanism to achieve multi-granularity scene modeling. This design not only meets the diverse granularity requirements of various tasks but also enhances nuanced cross-task feature interactions. Extensive experiments on two challenging benchmarks, i.e., NYUD-V2 and PASCAL-Context, show the superiority of our BIM vs its state-of-the-art competitors.