Dockless bike-sharing is an effective solution for the metro’s first- and last-mile connections. To create a more bicycle-friendly environment, there is a need to accurately predict the use of dockless bike–metro integration and understand its influencing factors. Previous studies have mainly focused on bike-metro integration at the metro station level, while we focus on the integration at a more refined resolution, i.e., the origin-destination level, which allows for more accurate measurement of the built environment factors and introduces the important factor of travel distance. Using 15 days of dockless bike-sharing data in part of Beijing, China, we propose a spatial embedding model based on graph convolution and improve the prediction performance of integrated flow. Additionally, we use XGBoost and SHapley Additive exPlanations (SHAP) to interpret the effects of the route, metro station, and built environment factors on the integrated flow. The travel distance, the number of commercial Point-of-Interests, the metro ridership, and the distance to the city center are found to be the most influential factors. Suggestions for improving the bicycle infrastructure are made based on these findings.