Bike-sharing for integrated public transport systems (BIPTS) offers an effective solution to the first- and last-mile problems. However, most existing studies have used overly simplified single-catchment area methods to identify BIPTS demands, and the driving factors and mobility patterns of BIPTS commuting demands have remained unclear. To fill this gap, a comprehensive framework for analyzing BIPTS commuting demands is developed. The proposed framework integrates a multi-catchment area method for precise BIPTS demands identification, the SHapley Additive exPlanations (SHAP) approach for uncovering driving factors, and a combination of dimensionality reduction and clustering techniques for discerning mobility patterns, complemented by a validation mechanism. A case study in Beijing demonstrates the efficacy of our multi-catchment areas method, which reduces misidentification of BIPTS demands by 48.6%. Notably, for morning peak first-mile demands, the driving factors are the available bike density of cycling catchment area, the bikeability index, and the metro passenger inflow. Strong factors interactions are observed, stemming from an imbalance between BIPTS demands and infrastructure supply. Additionally, three distinct commuting patterns emerge, attributed to variations in feature contributions. These insights are crucial for enhancing the seamless integration of bike-sharing and public transport systems.