Cold-start bundle recommendation focuses on modeling new bundles with insufficient information to provide recommendations. Advanced bundle recommendation models usually learn bundle representations from multiple views (e.g., interaction view) at both the bundle and item levels. Consequently, the cold-start problem for bundles is more challenging than that for traditional items due to the dual-level multi-view complexity. In this paper, we propose a novel Mixture of Diffusion Experts (MoDiffE) framework, which employs a divide-and-conquer strategy for cold-start bundle recommendation and follows three steps:(1) Divide: The bundle cold-start problem is divided into independent but similar sub-problems sequentially by level and view, which can be summarized as the poor representation of feature-missing bundles in prior-embedding models. (2) Conquer: Beyond prior-embedding models that fundamentally provide the embedded representations, we introduce a diffusion-based method to solve all sub-problems in a unified way, which directly generates diffusion representations using diffusion models without depending on specific features. (3) Combine: A cold-aware hierarchical Mixture of Experts (MoE) is employed to combine results of the sub-problems for final recommendations, where the two models for each view serve as experts and are adaptively fused for different bundles in a multi-layer manner. Additionally, MoDiffE adopts a multi-stage decoupled training pipeline and introduces a cold-start gating augmentation method to enable the training of gating for cold bundles. Through extensive experiments on three real-world datasets, we demonstrate that MoDiffE significantly outperforms existing solutions in handling cold-start bundle recommendation. It achieves up to a 0.1027 absolute gain in Recall@20 in cold-start scenarios and up to a 47.43\% relative improvement in all-bundle scenarios.