Topology optimization of bridge structures is challenging due to the difficulty in accounting for the stochastic dynamic nature of the moving vehicle loads. As a result, optimization for this common type of structure and loading is limited in the existing literature. Existing topology optimization approaches for addressing stochastic dynamic loading can be classified as time domain, frequency domain, or random vibration methods. Herein, a new compact representation of random moving traffic loading as a filtered white noise is developed which enables stochastic topology optimization to be performed. This optimization utilizes an objective function which combines the mean and standard deviation of responses to minimize the extreme response to random traffic loading. Examples show a significant improvement of the bridge response, represented by a reduction in the standard deviation at a minimal cost to the mean response. Also, optimal topologies for different traffic parameters such as speed and arrival rate are relatively similar, indicating a robust solution. With this approach, bridge topology can be efficiently optimized for random moving traffic loading by enabling direct minimization of response extremes, which represents the probabilistic design intent to achieve adequate levels of performance under the loading uncertainties in typical bridges.