Accurate brain tumor segmentation is significant for clinical diagnosis and treatment. It is challenging due to the heterogeneity of tumor subregions. Mamba-based State Space Models have demonstrated promising performance. However, they incur significant computational overhead due to sequential feature computation across multiple spatial axes. Moreover, their robustness across diverse BraTS data partitions remains largely unexplored, leaving a critical gap in reliable evaluation. To address these limitations, we propose dual-resolution bi-directional Mamba (DRBD-Mamba), an efficient 3D segmentation model that captures multi-scale long-range dependencies with minimal computational overhead. We leverage a space-filling curve to preserve spatial locality during 3D-to-1D feature mapping, thereby reducing reliance on computationally expensive multi-axial feature scans. To enrich feature representation, we propose a gated fusion module that adaptively integrates forward and reverse contexts, along with a quantization block that discretizes features to improve robustness. In addition, we propose five systematic folds on BraTS2023 for rigorous evaluation of segmentation techniques under diverse conditions and present detailed analysis of common failure scenarios. On the 20\% test set used by recent methods, our model achieves Dice improvements of 0.10\% for whole tumor, 1.75\% for tumor core, and 0.93\% for enhancing tumor. Evaluations on the proposed systematic five folds demonstrate that our model maintains competitive whole tumor accuracy while achieving clear average Dice gains of 0.86\% for tumor core and 1.45\% for enhancing tumor over existing state-of-the-art. Furthermore, our model attains 15 times improvement in efficiency while maintaining high segmentation accuracy, highlighting its robustness and computational advantage over existing approaches.