Cycling accessibility is a key indicator of urban resource equity and built environment performance. However, its relationship with equity, the importance of built environment factors, and nonlinear effects across facility types remain underexplored. This study combines the Gini coefficient with a generalized additive model (GAM) to examine the nonlinear accessibility–equity relationship and uses Light Gradient Boosting Machine (LightGBM) with SHapley Additive exPlanations (SHAP) to assess the importance and nonlinear effects of built environment variables. Potential effects of vegetation (Normalized Difference Vegetation Index, NDVI) and precipitation are also explored. Results show that both accessibility and equity peak in urban cores and decline toward peripheral areas. Facility types exhibit distinct patterns: accommodation services have high accessibility but low equity, life services require higher accessibility to achieve equity, and public services show an N-shaped relationship. SHAP analyses indicate that traffic signals, subway station accessibility, and street enclosure ratio are associated with higher cycling accessibility, whereas a higher sky view index is associated with lower accessibility. Observed moderating effects of vegetation and precipitation provide further insights into potential interactions. These findings offer guidance for improving cycling infrastructure and promoting more equitable and sustainable urban accessibility.