A reliable prognostics framework is essential to prevent catastrophic failure of bridges due to scour. In the U.S., scour accounts for almost 60% of bridge failures. Currently available techniques in the literature for predicting scour are mostly based on empirical equations and deterministic regression models, like Neural Networks and Support Vector Machines, and do not predict the evolution of scour over time. In this paper, we will discuss a Gaussian process model, which includes Bayesian uncertainty for prediction of time-dependent scour evolution. We will validate the model on the experimental data conducted in four different flumes in different conditions. The robustness of the algorithm will also be demonstrated under different scenarios, like lack of training data and equilibrium scour conditions. The results indicate that the algorithm is able to predict the scour evolution with an error of less than 20% for most of the time, and 5% or less given enough training data.