The automation of digital twinning for existing bridges from point clouds has yet been solved. Whilst current methods can automatically detect bridge objects in points clouds in the form of labelled point clusters, the fitting of accurate 3D shapes to detected point clusters remains human dependent to a great extent. 95% of the total manual modelling time is spent on customizing shapes and fitting them to right locations. The challenges exhibited in the fitting step are due to the irregular geometries of existing bridges. Existing methods can fit geometric primitives such as cuboids and cylinders to point clusters, assuming bridges are made up of generic shapes. However, the produced geometric digital twins are too ideal to depict the real geometry of bridges. In addition, none of existing methods have evaluated the resulting models in terms of spatial accuracy with quantitative measurements. We tackle these challenges by delivering a slicing-based object fitting method that can generate the geometric digital twin of an existing reinforced concrete bridge from labelled point clusters. The accuracy of the generated models is gauged using distance-based metrics. Experiments on ten bridge point clouds indicate that the method achieves an average modelling distance smaller than that of the manual one (7.05 cm vs. 7.69 cm) (value included all challenging cases), and an average twinning time of 37.8 seconds. Compared to the laborious manual practice, this is much faster to twin bridge concrete elements.