Dynamic wireless power transfer (DWPT) technology offers the promise of eliminating the limited driving range of electric buses (EBs), providing greater convenience and safety benefits through the ability to charge EBs in motion. It may be possible to effectively circumvent the drawbacks of EBs such that it becomes mainstream in the future EB market. In this paper, we study the robust DWPT deployment problem for an EB system, aiming to determine the DWPT facility deployment, battery size, and en-route charging schedule simultaneously. We first formulate the deterministic problem as a novel mixed-integer linear programming (MILP) model. Next, we consider the energy consumption uncertainty and travel time uncertainty to develop a two-stage robust model. We further analyze the structural properties of our proposed model, and implement the column-and-constraint generation (C&CG) method to solve it optimally. Finally, a series of experiments based on a test bus network and the National University of Singapore internal bus network are carried out to verify the efficiency and effectiveness of our models and algorithms. Some managerial insights are also provided that public transit (PT) operators could use to enhance the efficiency of the EB system in the future.