Climate change has the potential to significantly impact transportation infrastructure performance. Bridges crossing rivers are designed to withstand a maximum flood level (design flood) considering the expected frequencies and magnitudes of floods in the area. The design flood level ensures the safety of the bridge without being damaged against historical flooding levels. However, flood magnitude and/or frequency are expected to increase in some regions due to climate change, and therefore, bridges may not be able to maintain their serviceability and safety, resulting in significant risk to users and economic losses. This problem is approached in this paper by investigating the effects of flooding and climate change on bridges crossing rivers and surrounding areas. The input of the proposed methodology is the river flow for various climate change scenarios as well as the topography and bridge characteristics. Flood frequency analysis is used to provide information about the magnitude and frequency of annual maximum river discharges under a changing climate. Afterwards, several risk assessment indicators are computed for the bridge and its surrounding area. In addition, stochastic Poisson process is integrated to account for the randomness of floods arrivals and to investigate stochastically the probability of exceeding the design flood level. The proposed methodology is illustrated with a case study in the United Kingdom. The results indicate that the risk of flooding, and associated consequences, would increase for the case study when considering more pessimistic climate change scenarios. Findings from this study can be used to inform decision making for improving bridges’ resilience.