Unmanned aerial vehicle (UAV) image survey has been widely recognized as an effective method for capturing the status of bridges by photo-realistic 3D reconstruction. The reconstructed models contain rich geometric and textural information, which can be used to create digital twins, such as BIM-based or FEM-based ones. However, manual creation of such digital twins is tedious, and automated extraction of structural components and their geometry suffers from errors when the 3D reconstruction is imperfect or incomplete, requiring significant manual pre-processing of the raw data. To address this challenge, this research investigates an inverse parametric approach. First, a parametric generator of bridges, termed Random Bridge Generator (RBG) is developed. The RBG can generate photo-realistic synthetic models of six different types of bridges randomly and automatically. Those synthetic environments are used to simulate UAV-based image collection activities. The collected data is further processed to obtain realistic point cloud data with geometric and semantic ground truth data. Using the synthetic point cloud datasets and unsupervised domain adaptation techniques, a deep learning-based point cloud instance segmentation algorithm that can extract the critical structural components is developed. The segmentation results demonstrate the potential for fully automated bridge geometric digital twinning by estimating the parameters for the parametric bridge generator (RBG). The proposed approach is first evaluated using the synthetic point cloud dataset, followed by the preliminary evaluation using real-world point cloud data.