Bundle recommendation aims to provide users with a one-stop service by offering a collection of related items. However, these systems face a significant challenge, where a small portion of bundles accumulate most interactions while the long-tail bundles receive few interactions.This imbalance leads to poor performance for long-tail bundles despite their potential to satisfy diverse user needs. Existing long-tail item recommendation methods fail to effectively address this problem, as long-tail bundle recommendation requires not only capturing the user-bundle interactions but also the item compositions in different bundles. Therefore, in this paper, we propose Composition-Aware Long-tail Bundle Recommendation (CALBRec), which leverages the inherent composition patterns shared across different bundles as valuable signals for further representation augmentation and recommendation enhancement. Specifically, to solve the complexity of modeling shared composition patterns due to the exponential explosion caused by the growing number of items and bundle sizes, we first introduce a composition-aware tail adapter to capture the shared composition patterns and then adaptively integrate them into individual bundle representations. Moreover, to mitigate the impact of noise in user-bundle interaction data, we propose to map the bundle representations into a set of learnable prototypes, and we further propose a prototype learning module to combine the composition patterns with interaction signals for tail bundles. Extensive experiments on three public datasets demonstrate that our method can improve the performance on bundle recommendation significantly, especially on the long-tail bundles.