We introduce a physics-guided signal processing approach to extract a damage-sensitive and domain-invariant (DS & DI) feature from acceleration response data of a vehicle traveling over a bridge to assess bridge health. Motivated by indirect sensing methods' benefits, such as low-cost and low-maintenance, vehicle-vibration-based bridge health monitoring has been studied to efficiently monitor bridges in real-time. Yet applying this approach is challenging because 1) physics-based features extracted manually are generally not damage-sensitive, and 2) features from machine learning techniques are often not applicable to different bridges. Thus, we formulate a vehicle bridge interaction system model and find a physics-guided DS & DI feature, which can be extracted using the synchrosqueezed wavelet transform representing non-stationary signals as intrinsic-mode-type components. We validate the effectiveness of the proposed feature with simulated experiments. Compared to conventional time- and frequency-domain features, our feature provides the best damage quantification and localization results across different bridges in five of six experiments.