Modeling violin bridge admittance is a long-standing problem in musical acoustics, with applications in sound analysis, synthesis, and virtual instrument design. In this work, we investigate the use of the Eigensystem Realization Algorithm (ERA) for deriving reduced-order state-space models directly from measured impulse responses. The proposed approach allows us to extract dominant system dynamics and obtain compact realizations without requiring explicit modal parameterization. We evaluate ERA on a dataset of modern and historical violins and compare it against established modal and state-space identification methods. Experimental results demonstrate that ERA outperforms existing approaches by achieving lower reconstruction errors in both the time and frequency domains while preserving perceptually relevant characteristics of the bridge response. Furthermore, we show that the state-space realizations obtained using ERA reproduce the target frequency-dependent energy decay more accurately than models obtained using the baseline methods. These findings support the use of ERA as an efficient and flexible alternative for modeling violin bridge admittances, with applications that span from audio synthesis and processing to instrument virtualization.