To study how varying the parameters of expansion joints and bearing supports (E-B parameters) affects the dynamic response of a coupled vehicle–bridge system for curved girder bridges, a dynamic response analysis method for the coupled vehicle–joint (bearing)–bridge system, which takes into account centrifugal forces, was proposed and verified. Subsequently, taking a continuous curved box girder bridge as the prototype, the influence of the E-B parameters on the vehicle-induced dynamic response of the curved girder bridge was explored. The results showed that the dynamic amplification factor (DAF) of the middle beam of the expansion joint (DAF-EJ) and the main girder of the curved bridge (DAF-MG) were both significantly influenced by the E-B parameters. When there were height differences between the middle beam and side beam in the EJ, the DAF-EJ obviously varied, and the DAF-MG increased. When the EJ was damaged, the impact effect of the vehicle on the bearing support increased. The DAF-EJ and DAF-MG both increased with the decrease of the vertical support stiffness of the bearing support. The DAF-EJ was greatly affected by the single-support void at the near-slit end of the lane. The DAF-MGs at the beam end, the 1/4 point and 1/2 point of the first span, and the 1/2 point of the second span, were significantly affected by the single-support void near the measuring point. Compared with the single-support void, the DAF-EJ and DAF-MG more significantly increased under the double-support void. Variation in the height difference of the EJ had a more significant effect on the DAF-EJ and DAF-MG at the beam end, while a vertical stiffness reduction in the bearing support had a more significant effect on the DAF-MG.