The problem of vibration in urban rail transportation has become a current research hotspot. When a train passes through a bridge line at high speed, it interacts with the rail, leading to vibration energy transfer and causing issues such as vibration and noise in the line infrastructure. To propose a more targeted vibration-damping track structure, it is necessary to explore the vibration characteristics of urban rail transit bridge lines and understand the regulations governing the distribution of vibration energy. This paper employs the theory of vehicle–rail–bridge interaction to establish a coupled dynamics model for a subway A-type vehicle–integral ballast bed–box girder bridge. Based on the proposed model, the transmission characteristics and distribution of vibration energy in the rail–bridge system are systematically analyzed and the influence of the parameters of the track structural components on the power flow of the system are investigated. The results of this study indicate that low-frequency vibration energy in the track system of urban rail transit bridges is primarily concentrated within the track structure, whereas high-frequency vibration energy is mainly focused on the rail. The fastener, as a component connecting the rail and the overall roadbed, has different effects on the peak value of the power flow and the accumulation of vibration energy in various components such as the rail, the overall roadbed, the top plate of the box girder bridge, and the bottom plate in different frequency bands due to its own stiffness and damping. An appropriate increase in fastener damping is beneficial for reducing the accumulation of low-frequency vibration energy in the track structure.