Drive-by Health Monitoring utilizes accelerometers mounted on vehicles to gather dynamic response data that can be used to continuously evaluate the health of bridges faster and with less equipment than traditional structural health monitoring practices. Because vehicles and bridges create a coupled system, vehicle acceleration data contains information about bridge frequencies that can be used as health indicators. However, for drive-by health monitoring to be viable, variabilities in dynamic measurements caused by environmental and operational parameters, such as temperature, vehicle speed, traffic, and surface roughness need to be considered. In this paper, a finite element model of a simply supported bridge is developed considering the aforementioned variabilities and various levels of structural damage. Vehicle acceleration data obtained from the model is analyzed in the frequency domain and processed using a neural network architecture. This method is used to determine the relationships between noise inducing variables and changes in vehicle dynamic response spectrum; these relationships are leveraged to predict the overall health of the subject bridge. The results from this study indicate that the proposed approach can serve as a viable health monitoring strategy and should be further tested on physical bridge systems.