A nonlinear dynamic model of a train–bridge-longitudinal track coupling system considering the dynamic contact of the bridge–track interface (BTI) is established. Based on the previously established BTI contact characterization model and train–bridge coupling joint simulation model, the proposed model is verified from both static and dynamic perspectives. Accordingly, the dynamic displacement variation law of the bridge–track structure before, during and after the train passing through the side pier settlement area, the additional stress dynamic variation law and the interlayer connection dynamic variation law are analyzed. Moreover, the amplification effect of the wheel repeated “beating effect” on the dynamic contact force of “disengagement-closure-redisengagement” of the BTI void area is also analyzed. The results show that the accuracy of the proposed model can be verified from both static and dynamic perspectives. During the train passes through the settlement area, the dynamic deformation of track is the largest. Before and after the train passes through the settlement area, the dynamic deformation of track is basically the same. During the train passes through the settlement area, the BTI completes a dynamic contact process of “disengagement-closure-redisengagement”. The static effect of the side pier settlement on the dynamic bonding force of sliding layer is much larger than the dynamic effect of the train load. The dynamic effect of the train load is much larger than the static effect of the side pier settlement on the dynamic bonding force of the CA mortar and fasteners. The side pier settlement has a dynamic amplification effect on the train wheelset. Along the mileage direction, there are interface voids and contact areas in the dynamic bonding force of sliding layer and CA mortar, while there are no voids and contact areas in the dynamic bonding force of fasteners.