Coastal areas worldwide are experiencing a profound impact from climate change, with transportation systems along the coastline being particularly vulnerable. Failure of bridges may severely disrupt the serviceability of transportation networks, causing considerable economic and social losses. The extensive destruction caused by the Nova Scotia Flood in 2023 is a stark reminder of the impact of climate change on the Atlantic coastal regions of Canada, where extreme weather events, particularly flooding, continue to occur with increasing frequency and intensity. The increased flooding leads to higher riverbed erosion and scours around bridge foundations, exacerbating the risk of bridge collapse. To address these challenges, this study presents a risk-based assessment framework that integrates component-level analyses, including the estimation of scour depth based on climate conditions and bridge age, with network-level considerations like potential detour lengths necessitated by bridge failures. Particular focus of this study is the development of a deep learning model that seeks to understand the dynamics between climate variables (temperature and precipitation) and streamflow patterns. This model is then applied to forecast future streamflow and to assess the potential risk of bridge damage from water erosion at abutments under different climate scenarios. When this approach is applied to the examination of bridges in Nova Scotia, it reveals a heightened risk of failure due to flood-induced scour, emphasizing the necessity for strategic adaptation planning and the prioritization of bridge maintenance to enhance resilience against future climate threats. These findings offer a preliminary and exploratory analysis focused on quantifying the negative effects of climate change on bridges, from individual infrastructure components to the broader transportation network.