Low-cost, DC micro-electromechanical systems (MEMS) accelerometers can be employed to provide a mechanism to capture the relatively small levels of rotation typically seen on some bridges allowing their structural response to be measured. The effect of ambient vehicle traffic loads crossing the bridge can offer a cost-effective, less disruptive alternative method for continuous bridge structural health monitoring (BSHM). However, utilising moving traffic loads to assess the quasi-static structural behaviour is more challenging as the measured sensor data contains additional signal components due to the dynamics of the vehicle-bridge interaction system. To overcome this challenge, this paper presents a simplified approach for the specification of an appropriate filtering scheme to extract the desired quasi-static bridge response based on only the bridge's geometry and the vehicle speed. The originality of the method proposed herein lies in its wide applicability and extensibility due to its basis on the widely accepted principles of bridge influence lines. For both BSHM researchers and practitioners alike, the significance of the proposed method lies in its systematic approach, thus helping to unlock the potential for long-term monitoring of bridge quasi-static response under ambient traffic loading. The approach is demonstrated through its successful application in a field trial on an in-service highway bridge.