This paper proposes a novel control framework for agile and robust bipedal locomotion, addressing model discrepancies between full-body and reduced-order models. Specifically, assumptions such as constant centroidal inertia have introduced significant challenges and limitations in locomotion tasks. To enhance the agility and versatility of full-body humanoid robots, we formalize a Model Predictive Control (MPC) problem that accounts for the variable centroidal inertia of humanoid robots within a convex optimization framework, ensuring computational efficiency for real-time operations. In the proposed formulation, we incorporate a centroidal inertia network designed to predict the variable centroidal inertia over the MPC horizon, taking into account the swing foot trajectories -- an aspect often overlooked in ROM-based MPC frameworks. By integrating the MPC-based contact wrench planning with our low-level whole-body controller, we significantly improve the locomotion performance, achieving stable walking at higher velocities that are not attainable with the baseline method. The effectiveness of our proposed framework is validated through high-fidelity simulations using our full-body bipedal humanoid robot DRACO 3, demonstrating dynamic behaviors.