Bridges are vital infrastructures but face compounding risks from scouring and seismic events. Although recent studies have explored these individual and overlapping hazards, they often utilize deterministic approaches and focus on specific bridge types in limited geographical areas. This study addresses these gaps by introducing a probabilistic framework for assessing the seismic performance of multi-span reinforced concrete (RC) highway bridges in the presence of scour-related uncertainties. A time-dependent scour model, informed by a Bayesian approach and literature-based uncertainties, is integrated into the framework. Probabilistic Seismic Hazard Analysis (PSHA) and record selection strategies are employed to define the seismic demand probabilistically. Monte Carlo simulation (MCS) is utilized to propagate combined uncertainties during the analysis, considering different scour scenarios defined according to the discharge peak condition of the flood event at the specific location of the bridge. In the last step of the probabilistic framework, fragility analyses are conducted on individual components and the entire system by means of nonlinear dynamic models and multiple stripe analysis (MSA). An actual five-span bridge with simply supported prestressed concrete girders, located in Chile, is used as application example of the proposed approach, considering measured hydrological data and seismic hazard of the real location of the bridge. The study identifies distinct vulnerabilities across various bridge components under scour conditions. Elastomeric bearings are particularly susceptible in scenarios characterized by low scour depths (low discharge peak condition). Conversely, abutments display heightened vulnerabilities as scour depth increases (medium discharge peak condition). Piles also exhibit notable vulnerability, escalating in scenarios with great scour depth (medium discharge peak condition). Notably, piles tend to be more susceptible than columns to scour effects, especially in bents featuring shorter columns. These disparities in vulnerability are influenced by the bridge design philosophy, as well as the synergistic effects of seismic forces and varying scour depths. System fragility curves further elucidate that the likelihood of exceeding specific damage thresholds varies according to different scour scenarios, with the deeper scour depth scenario, displaying the higher vulnerabilities.