Bundle recommendation aims to suggest a set of interconnected items to users. However, diverse interaction types and sparse interaction matrices often pose challenges for previous approaches in accurately predicting user-bundle adoptions. Inspired by the distant supervision strategy and generative paradigm, we propose BRIDGE, a novel framework for bundle recommendation. It consists of two main components namely the correlation-based item clustering and the pseudo bundle generation modules. Inspired by the distant supervision approach, the former is to generate more auxiliary information, e.g., instructive item clusters, for training without using external data. This information is subsequently aggregated with collaborative signals from user historical interactions to create pseudo `ideal' bundles. This capability allows BRIDGE to explore all aspects of bundles, rather than being limited to existing real-world bundles. It effectively bridging the gap between user imagination and predefined bundles, hence improving the bundle recommendation performance. Experimental results validate the superiority of our models over state-of-the-art ranking-based methods across five benchmark datasets.