In recent years, overturning accidents of box girder bridges have occurred frequently, causing widespread concern among researchers. From the perspective of bridge structure monitoring, this paper presents two technical routes for evaluating the risk of potential overturning risk of a bridge: (1) traffic loads monitoring based on an anti-overturning stability coefficient and (2) structural response monitoring based on the control of a bearing’s rotational angle. For the second route, a simple and feasible monitoring scheme is presented depending on the structural response—displacement of measured points on both sides of bearings. Then, a method to assess bridge anti-overturning reliability is proposed. The influence of aging of rubber material on the rotation performance of a bearing is further considered. Finally, the study applied the method described above to an anti-overturning analysis of the Northeast Ramp Bridge at Tongji Road in Shanghai, which demonstrated the method’s feasibility and effectiveness.