We propose a control framework that integrates model-based bipedal locomotion with residual reinforcement learning (RL) to achieve robust and adaptive walking in the presence of real-world uncertainties. Our approach leverages a model-based controller, comprising a Divergent Component of Motion (DCM) trajectory planner and a whole-body controller, as a reliable base policy. To address the uncertainties of inaccurate dynamics modeling and sensor noise, we introduce a residual policy trained through RL with domain randomization. Crucially, we employ a model-based oracle policy, which has privileged access to ground-truth dynamics during training, to supervise the residual policy via a novel supervised loss. This supervision enables the policy to efficiently learn corrective behaviors that compensate for unmodeled effects without extensive reward shaping. Our method demonstrates improved robustness and generalization across a range of randomized conditions, offering a scalable solution for sim-to-real transfer in bipedal locomotion.