Bundle recommendation aims to accurately predict the probabilities of user interactions with bundles. Most existing effective methods learn the embeddings of users and bundles from user-bundle interaction view and user-item-bundle interaction view. However, they seldom leverage the recommendation difference caused by the distinct learning trends of two views when modeling user preferences. Meanwhile, such two view interaction graphs are typically tree-like. If the graph data with this structure is embedded in Euclidean space, it will lead to severe distortion problem. To this end, we propose a novel Hyperbolic Mutual Learning model for Bundle Recommendation (HyperMBR). The model encodes the entities (user, item, bundle) of the two view interaction graphs in hyperbolic space to learn their accurate representations. Furthermore, a mutual distillation based on hyperbolic distance is proposed to encourage the two views to transfer knowledge for increasingly improving the recommendation performance. Extensive empirical experiments on two real-world datasets confirm that our HyperMBR achieves promising results compared to state-of-the-art bundle recommendation methods.