Bridges are an essential component of the land transport system. The performance of the bridge structures plays a crucial role during extreme events such as an earthquake to perform rehabilitation and relief activities. Hence the safety of bridge structures during seismic events needs to be ensured. Various devices have been proposed and implemented into the bridge construction to ensure the seismic safety of the bridges. The base isolation system proved to be an efficient device to mitigate the bridge response when subjected to earthquake loading. In the present study, an inerter device has been employed in conjunction with base isolation between deck and pier. The optimal parameters of the damper are obtained by performing a stochastic optimization study. Further, the damper efficiency is verified by conducting a time history analysis by subjecting the bridge structure to a set of recorded ground motions. The application of inerter device, in conjunction with the base isolation system, has significantly improved the efficiency and robustness of the base isolation system in reducing structural response.