Probabilistic Seismic Hazard Assessment (PSHA) evaluates the probability of exceedance of a given earthquake intensity threshold like the Peak Ground Acceleration, at a target site for a given exposure time. The stochasticity of the occurrence of seismic events is modelled by stochastic processes and the propagation of the earthquake wave in the soil is typically evaluated by empirical relationships called Ground Motion Prediction Equations. The large uncertainty affecting PSHA is quantified by defining alternative model settings and/or model parametrizations. In this work, we propose a novel Bootstrapped Modularised Global Sensitivity Analysis (BMGSA) method for identifying the model parameters most important for the uncertainty in PSHA, that consists in generating alternative artificial datasets by bootstrapping an available input-output dataset and aggregating the individual rankings obtained with the modularized method from each of those. The proposed method is tested on a realistic PSHA case study in Italy. The results are compared with a standard variance-based Global Sensitivity Analysis (GSA) method of literature. The novelty and strength of the proposed BMGSA method are both in the fact that its application only requires input-output data and not the use of a PSHA code for repeated calculations.