Bridge information models are essential for bridge inspection, assessment, and management. LiDAR technology, particularly UAV LiDAR, offers a cost-effective means to capture dense and accurate 3D coordinates of a bridge's surface. However, the structure of large-scale bridges is complex, and existing commercial software still demands substantial manual effort to segment the components when constructing bridge information models for large-scale bridges. This study introduces a novel approach to automatically segment the components of a long-span rail-and-road cable-stayed bridge from the entire point cloud obtained through UAV LiDAR. In this proposed approach, the geometric and topological constraints of various bridge components are thoroughly examined, and a combination of the coarse-to-fine concept and top-down strategy is employed. The key structural elements, including piers, cable towers, wind fairing plate, stay-cable, main truss, railway surfaces, and deck surfaces, are identified and segmented. The proposed methodology achieves an average accuracy of over 96% at the point level validated using datasets acquired by UAV LiDAR.