A computational efficient Bayesian inference framework based on stochastic simulation algorithms is presented for calibrating the parameters of large-order linear finite element (FE) models of bridges. The effectiveness of stochastic simulation tools to handle large-order linear models in Bayesian analysis is demonstrated by calibrating a high fidelity FE model of the Metsovo bridge with several hundreds of thousands of DOF, using experimentally identified modal frequencies and mode shapes based on ambient vibration measurements collected from a wireless mobile measuring system. The mode shapes of the bridge are assembled using the identified modal characteristics from a number of different sensor configurations, involving reference and moving sensors, optimally placed on the bridge deck to adequately cover the whole bridge span. The identified finite element models and their uncertainties are representative of the initial structural condition of the bridge and can be further used for structural health monitoring purposes.