The prediction of bike-sharing demand plays a pivotal role in the optimization of intelligent transportation systems, particularly amidst the COVID-19 pandemic, which has significantly altered travel behaviors and demand dynamics. In this study, we examine various spatiotemporal influencing factors associated with bike-sharing and propose the Local-Global Dynamic Multi-Graph Convolutional Network (LGDMGCN) model, driven by multi-source data, for multi-step prediction of station-level bike-sharing demand. In the temporal dimension, we dynamically model temporal dependencies by incorporating multiple sources of time semantic features such as confirmed COVID-19 cases, weather conditions, and holidays. Additionally, we integrate a time attention mechanism to better capture variations over time. In the spatial dimension, we consider factors related to the addition or removal of stations and utilize spatial semantic features, such as urban points of interest and station locations, to construct dynamic multi-graphs. The model utilizes a local-global structure to capture spatial dependencies among individual bike-sharing stations and all stations collectively. Experimental results, obtained through comparisons with baseline models on the same dataset and conducting ablation studies, demonstrate the feasibility and effectiveness of the proposed model in predicting bike-sharing demand.