In this paper, we address the challenges in automatic sleep stage classification, particularly the high computational cost, inadequate modeling of bidirectional temporal dependencies, and class imbalance issues faced by Transformer-based models. To address these limitations, we propose BiT-MamSleep, a novel architecture that integrates the Triple-Resolution CNN (TRCNN) for efficient multi-scale feature extraction with the Bidirectional Mamba (BiMamba) mechanism, which models both short- and long-term temporal dependencies through bidirectional processing of EEG data. Additionally, BiT-MamSleep incorporates an Adaptive Feature Recalibration (AFR) module and a temporal enhancement block to dynamically refine feature importance, optimizing classification accuracy without increasing computational complexity. To further improve robustness, we apply optimization techniques such as Focal Loss and SMOTE to mitigate class imbalance. Extensive experiments on four public datasets demonstrate that BiT-MamSleep significantly outperforms state-of-the-art methods, particularly in handling long EEG sequences and addressing class imbalance, leading to more accurate and scalable sleep stage classification.