The cost and effort for modelling existing bridges from point clouds currently outweighs the perceived benefits of the resulting model. Automating the point cloud-to-Bridge Information Models process can drastically reduce the manual effort and cost involved. Previous research has achieved the automatic generation of surfaces primitives combined with rule-based classification to create labelled construction models from point clouds. These methods work very well in synthetic dataset or idealized cases. However, real bridge point clouds are often incomplete, and contain unevenly distributed points. Also, bridge geometries are complex. They are defined with horizontal alignments, vertical elevations and cross-sections. These characteristics are the reasons behind the performance issues existing methods have in real datasets. We propose to tackle this challenge via a novel top-down method for major bridge component detection in this paper. Our method bypasses the surface generation process altogether. Firstly, this method uses a slicing algorithm to separate deck assembly from pier assemblies. It then detects pier caps using their surface normal, and uses oriented bounding boxes and density histograms to segment the girders. Finally, the method terminates by merging over-segments into individual labelled point clusters. Experimental results indicate an average detection precision of 99.2%, recall of 98.3%, and F1-score of 98.7%. This is the first method to achieve reliable detection performance in real bridge datasets. This sets a solid foundation for researchers attempting to derive rich IFC (Industry Foundation Classes) models from individual point clusters.