A bridge may displace due to various loadings (e.g., thermal (Xia et al. in Struct Control Health Monit 28(7):e2738, 2013), winds (Owen et al. in J Wind Eng Ind Aerodyn 206:104389, 2020), and vehicles (Xu et al. in J Struct Eng 133(1):3–11, 2007)) acting upon the bridge. Identifying the contributions of individual loading factors to the measured bridge displacements is important for understanding the structural health conditions of the bridge. There is however no effective method to quantify the contributions when multiple loadings act simultaneously on a bridge. We propose a new data-driven method, termed random forest (RF)-assisted variational mode decomposition (RF-AVMD), for more effective identification of dominant loading factors and for quantifying the contributions of individual loading factors to the measured bridge displacements. The proposed method is applicable to studying the displacements of any bridge structures and allows for the first time to separate the contributions of individual loadings. The effectiveness of the proposed method is validated using data from Tsing Ma Bridge (TMB), a large suspension bridge in Hong Kong recorded during two consecutive strong typhoons. The results reveal that the transverse displacements of TMB mid-span were controlled by the crosswinds, the longitudinal displacements were dominated by the temperature and winds along the bridge centerline, and the vertical displacements were mainly due to the winds along the bridge centerline, temperature, and traffic flows. Displacement time series that responded to each loading factor was derived. The proposed method provides important new insights into the impacts of individual loadings on the displacements of long-span bridges.