This paper presents a reactive control framework for robotic bipedal running over random discrete terrain using a shift-invariant funnel library that can be composed into motion plans. The main contribution of the paper is the formalization of the funnel library and the introduction of a receding-horizon reactive planner that utilizes this funnel library. The proposed controller generates a robust motion plan on the fly, without the need for predefined footholds or center of mass trajectory, via sequential-composition of pre-computed funnels. The proposed method utilizes three layers of robustness: high-level reactive planning, low-level robust control, and funnel-based, pre-computed, performance guarantees. For clarity, we provide a detailed example, using the 5 degrees-of-freedom sagittal biped model. We demonstrate in simulation the ability of the framework to overcome uncertainty in sensing and model parameters.