Accurate demand prediction is crucial for the equitable and sustainable expansion of bike-sharing systems, which help reduce urban congestion, promote low-carbon mobility, and improve transportation access in underserved areas. However, expanding these systems presents societal challenges, particularly in ensuring fair resource distribution and operational efficiency. A major hurdle is the difficulty of demand prediction at new stations, which lack historical usage data and are heavily influenced by the existing network. Additionally, new stations dynamically reshape demand patterns across time and space, complicating efforts to balance supply and accessibility in evolving urban environments. Existing methods model relationships between new and existing stations but often assume static patterns, overlooking how new stations reshape demand dynamics over time and space. To tackle these challenges, we propose a novel demand prediction framework for expanding bike-sharing systems, namely BGM, which leverages dynamic graph modeling to capture the evolving inter-station correlations while accounting for spatial and temporal heterogeneity. Specifically, we develop a knowledge transfer approach that studies the embeddings transformation across existing and new stations through a learnable orthogonal mapping matrix. We further design a gated selecting vector-based feature fusion mechanism to integrate the transferred embeddings and the intrinsic features of stations for precise predictions. Experiments on real-world bike-sharing data demonstrate that BGM outperforms existing methods.