Scouring of bridge piers is a major cause of bridge failure worldwide. Thus, designing safe depths for new bridge foundations and assessing/monitoring the safety of existing bridge foundations are critical to reducing the risk of bridge collapse and the subsequent potential losses in terms of life and property. This paper develops and tests the evolutionary radial basis function neural network (ERBFNN) as a model to forecast scour depth at bridge piers. The ERBFNN is an artificial intelligence (AI) inference model that integrates the radial basis function neural network (RBFNN) and the artificial bee colony (ABC). In the ERBFNN, the RBFNN handles the learning and fitting curves and ABC uses optimization to search for the optimal hidden neuron number and width of the Gaussian function. The performance of the ERBFNN is compared with four other AI techniques, including the back-propagation neural network (BPNN), genetic programming (GP), M5 regression tree (M5), and support vector machine (SVM). Further, the prediction accuracy of the ERBFNN is benchmarked against four prevalent mathematical methods, including the HEC-18 method, Mississippi’s method, Laursen and Toch’s method, and Froehlich’s method. Results of these comparisons demonstrate that the ERBFNN predicts scour depth at bridge piers with a degree of accuracy that is significantly better than current, widely used methods.