A hybrid methodology is presented for modelling aerodynamic forces on bluff bodies by combining the quasi-steady model with a Gaussian process that learns discrepancies caused by the quasi-steady assumption. The model uses nondimensional motion- and gust-induced angles of attack to predict probability distributions of lift and moment coefficients. Training data are generated through computational fluid dynamics with simultaneous structural motion and prescribed free-stream turbulence, and the model is assessed for large-amplitude forced vibration and buffeting response across several wind speeds.