Optimal routing solutions in deterministic models usually fail to deliver promised on-time services in the real world of uncertainty, causing potential loss of customers and revenue. In this study, we propose a new formulation for the data-driven Vehicle Routing Problem with Time Windows (VRPTW) under uncertain travel times that is compatible with the paradigm of distributionally robust optimization. An innovative decision criterion on the delays, termed the Service Fulfillment Risk Index (SRI) is proposed to accounts for both the late arrival probability and its magnitude, captures the risk and the Wasserstein ambiguity in travel times, and is efficiently evaluable in closed form. In particular, the closed-form solution reduces the VRPTW under the Wasserstein ambiguity of interest to the problem under the empirical distribution with advanced deadlines. In computational studies, our solution greatly improves on-time arrival performance with slightly increased expenditure than the deterministic solution. Our SRI also outperforms the canonical decision criteria, lateness probability and expected lateness duration, in out-of-sample simulations.