To investigate the impact of variable-speed vehicles on the creep of curved girder bridges, a typical ramp bridge was selected as a case study to analyze the influence of vehicle-related factors on this phenomenon. A finite element model of the curved bridge was developed using ANSYS, incorporating a solid main girder model and bilinear spring bearings. The validity of the computational model was verified through comparison with a MIDAS/Civil model. Moving vehicle loads were equivalently transformed into vertical loads superimposed with time-varying radial centrifugal forces. These loads were applied to the curved bridge model using shape functions to generate load files. Subsequently, vehicle-related factors affecting lateral displacement—including initial entry speed, acceleration/deceleration, and vehicle weight—were systematically analyzed. Results indicate that the lateral displacement at key bridge sections initially increases and then decreases as the radial force approaches and moves away from the key sections. Higher initial vehicle entry speeds and greater vehicle weights lead to increased lateral displacement of the main girder, vertical displacement at mid-span sections, vertical reaction forces of outer bearings, and transverse reaction forces of both inner and outer bearings. Conversely, higher initial entry speeds reduce vertical reaction forces of inner bearings. Larger deceleration magnitudes (absolute values) reduce lateral displacement but exhibit negligible effects on mid-span vertical displacement and bearing reactions. Vehicle entry speed and weight are identified as primary influencing factors for lateral displacement, while deceleration plays a secondary role.