Bridges are essential structures in the logistic chain of countries, making it critical to design them to be as resilient as possible. One way to achieve this is through performance-based seismic design (PBSD), which involves using nonlinear Finite Element (FE) models to predict the response and potential damage of different structural components under earthquake excitations. Nonlinear FE models need accurate constitutive models of material and components. Among them, seismic bars and laminated elastomeric bearings play an important role in a bridge’s response to earthquakes; therefore, properly validated and calibrated models should be proposed. Only default parameter values from the early development of the constitutive models widely used by researchers and practitioners for these components tend to be used, and low identifiability of its governing parameters and the high cost of generating reliable experimental data have prevented a thorough probabilistic characterization of their model parameters. To address this issue, this study implements a Bayesian probabilistic framework using Sequential Monte Carlo (SMC) for updating the parameters of constitutive models of seismic bars and elastomeric bearings and proposes joint probability density functions (PDF) for the most influential parameters. The framework is based on actual data from comprehensive experimental campaigns. The PDFs are obtained from independent tests conducted on different seismic bars and elastomeric bearings, to then consolidate all the information in a single PDF for each modeling parameter by means of the conflation methodology, where the mean, coefficient of variation, and correlation between calibrated parameters are obtained for each bridge component. Finally, findings show that the incorporation of model parameter uncertainty through a probabilistic framework will allow for a more accurate prediction of the response of bridges under strong earthquakes.