Assessing flood risks on road infrastructures is critical for the definition of mitigation strategies and adaptation processes. Some efforts have been made to conduct a regional flood risk assessment to support the decision-making process of exposed areas. However, these approaches focus on the physical damage of civil infrastructures without considering indirect impacts resulting from social aspects or traffic delays due to the functionality loss of transportation infrastructures. Moreover, existing methodologies do not include a proper assessment of the uncertainties involved in the risk quantification. This work aims to provide a consistent quantitative flood risk estimation and influence factor modelling for road infrastructures. To this end, a Flood Risk Factor (FRF) is computed as a function of hazard, vulnerability, and infrastructure importance factors. A Bayesian Network (BN) is constructed for considering the interdependencies among the selected input factors, as well as accounting for the uncertainties involved in the modelling process. The proposed approach allows weighting the relevant factors differently to compute the FRF and improves the understanding of the causal relations between them. The suggested method is applied to a case study located in the region of Santarem Portugal, allowing the identification of the sub-basins where the road network has the highest risks and illustrating the potential of Bayesian inference techniques for updating the model when new information becomes available.