The exponential surge in live video streaming during high-density simultaneous events imposes significant strain on 5G cellular architectures. While Unicast Adaptive Bitrate (UABR) streaming maximizes individual Quality of Experience (QoE), it entails excessive spectral redundancy. Conversely, conventional multicast improves resource efficiency but often compromises aggregate QoE by disregarding user-specific channel conditions and mobility. To bridge this gap, we propose MuLTEcast-Bandit, a lightweight contextual Multi-Armed Bandit (LinUCB) framework deployed at the Mobile Edge Computing (MEC) layer. The proposed algorithm dynamically optimizes the transmission paradigm, multicast versus unicast, and bitrate selection based on real-time network features, including group density, channel quality indicators, and client-side stall events. Simulation results demonstrate that MuLTEcast-Bandit significantly outperforms traditional benchmarks, achieving a 57% increase in mean QoE over static multicast and a 21% improvement over heuristic-based policies. Notably, the framework delivers these performance gains while utilizing only 58% of the bandwidth required by pure unicast deployments, effectively balancing peak individual quality with network-wide spectral efficiency. Furthermore, the solution’s low computational complexity ensures high deployability on modest edge hardware compared to heavy deep reinforcement learning alternatives. These findings delineate a scalable and energy-efficient path for multimedia orchestration in future green 6G network architectures, providing a robust policy for sustainable high-demand streaming.