This paper addresses the application of a Bayesian parameter estimation method to a regional seismic risk assessment of curved concrete bridges. For this purpose, numerical models of case-study bridges are simulated to generate multiparameter demand models of components, consisting of various uncertainty parameters and an intensity measure (IM). The demand models are constructed using a Bayesian parameter estimation method and combined with limit states to derive the parameterized fragility curves. These fragility curves are used to develop bridge-specific and bridge-class fragility curves. Moreover, a stepwise removal process in the Bayesian parameter estimation is performed to identify significant parameters affecting component demands.