The immense volume of user-generated video content demands scalable summarization methods that do not require costly human annotations. Unsupervised approaches provide this flexibility but still face key limitations: reliance on unimodal inputs, weak temporal modeling, and deterministic outputs that fail to capture uncertainty. To overcome these limitations, we propose MBSum, a novel unsupervised multimodal video summarization framework that leverages both visual and textual modalities without requiring labeled data. MBSum combines a Mamba-based state space backbone for efficient long-range temporal modeling with Bayesian variational decoder for a robust, uncertainty-aware summary generation. In addition, we propose a text-guided contrastive loss to align visual and textual features, enhancing cross-modal coherence. MBSum supports both unimodal and multimodal inputs, which makes it adaptable to diverse real-world scenarios. Extensive experiments on five benchmarks (TVSum, SumMe, Soccer, MLB, and LoL) demonstrate the effectiveness of MBSum, achieving state-of-the-art performances on all datasets.