Bridges serve as vital engineering structures crafted to facilitate secure and effective transportation networks. Throughout their life-cycle, they withstand various factors, including diverse environmental conditions, natural hazards, and substantial loads. Recent bridge failures underscore the significant risks posed to the structural integrity of bridges. Damage detection techniques, being core components of structural health monitoring, play a crucial role in objectively assessing bridge conditions. This article introduces a novel framework for identifying damage in bridges utilizing continuous wavelet analysis of accelerations recorded using two sensors mounted on a vehicle traversing the bridge. The proposed method leverages changes in the static response of the bridge, which has proven to be more sensitive to damage than its dynamic counterpart. By doing so, the method eliminates the reliance on modal parameters for damage identification, addressing a significant challenge in the field. The proposed framework also addresses key challenges encountered by drive-by monitoring methods. It mitigates the adverse effects of road roughness by utilizing residual accelerations and efficiently detects and locates damage even in the absence of corresponding data from an undamaged bridge. Numerical investigations demonstrate the robustness of the proposed method against various parameters, including damage location and extent, vehicle speeds, road roughness levels, different boundary conditions, and multi-damage scenarios.