Bagging operations, common in packaging and assisted living applications, are challenging due to a bag's complex deformable properties. To address this, we develop a robotic system for automated bagging tasks using an adaptive structure-of-interest (SOI) manipulation approach. Our method relies on real-time visual feedback to dynamically adjust manipulation without requiring prior knowledge of bag materials or dynamics. We present a robust pipeline featuring state estimation for SOIs using Gaussian Mixture Models (GMM), SOI generation via optimization-based bagging techniques, SOI motion planning with Constrained Bidirectional Rapidly-exploring Random Trees (CBiRRT), and dual-arm manipulation coordinated by Model Predictive Control (MPC). Experiments demonstrate the system's ability to achieve precise, stable bagging of various objects using adaptive coordination of the manipulators. The proposed framework advances the capability of dual-arm robots to perform more sophisticated automation of common tasks involving interactions with deformable objects.