The structure of the broad line region (BLR) is an essential ingredient in the determination of active galactic nuclei (AGN) virial black hole masses, which in turn are important to study the role of black holes in galaxy evolution. Constraints on the BLR geometry and dynamics can be obtained from velocity-resolved studies using reverberation mapping data (i.e. monitoring data). However, monitoring data are observationally expensive and only available for a limited sample of AGN, mostly confined to the local Universe. Here we explore a new version of a Bayesian inference, physical model of the BLR which uses an individual spectrum and prior information on the BLR size from the radius-luminosity relation, to model the AGN BLR geometry and dynamics. We apply our model to a sample of 11 AGN, which have been previously modelled using monitoring data. Our single-epoch BLR model is able to constrain some of the BLR parameters with inferred parameter values that agree within the uncertainties with those determined from the modelling of monitoring data. We find that our model is able to derive stronger constraints on the BLR for AGN with broad emission lines that qualitatively have more substructure and more asymmetry, presumably as they contain more information to constrain the physical model. The performance of this model makes it a practical and cost-effective tool to determine some of the BLR properties of a large sample of low and high redshift AGN, for which monitoring data are not available.