Rocking structures are recognized as an effective seismic response modification technique due to their peculiar dynamic characteristics. Meanwhile, in bridge structures, strong ground motions have frequently caused a rocking motion of pin bearings around their two toes, resulting in the pulling-out of anchor bolts. This study, motivated by the promising features of rocking behaviors, seeks to develop a rocking isolation bearing system (RIBS) to control excessive response in bridges. An example bridge featuring such a RIBS, consisting of the pin bearings removing anchor bolts to release the rocking motion, the girder-type superstructure, and an array of bridge piers, is characterized by a simplified model. Two coefficients of restitution (COR) models are used to investigate the effects of energy dissipation during impact: the Housner model, and a model which simultaneously modifies the velocities of the superstructure and substructures. The dynamic characteristics of RIBS and its control effectiveness on the bridge structure are discussed through a series of dynamic analyses, under both observed ground motions and the design ground motions specified in the Japan Road Association (JRA) design specifications for highway bridges. The simulation results demonstrate that the seismic performance of the bridge structure can be substantially improved, with decreased pier displacement at an allowable bearing rotation level.