Dynamic manipulation of deformable linear objects (DLOs) remains challenging due to underactuated, high-dimensional dynamics, delayed deformation responses, and the presence of multiple feasible motions under obstacle constraints. This paper presents BM2PC, a Bayesian Multimodal MPC framework for agile manipulation of DLOs. Building on the control-as-inference posterior, BM2PC formulates multimodal planning as a set optimization problem that balances control quality and behavioral diversity. An efficient incremental update maintains multiple promising control modes with low additional computational overhead. For real-world deployment, BM2PC incorporates an execution dynamics model that predicts actual end-effector motion and compensates for execution mismatch during fast manipulation. We evaluate BM2PC on rope tracking and obstacle avoidance in simulation and hardware, and on simulated disturbance rejection. In trajectory tracking, BM2PC generalizes better to unseen trajectories than a learning-based baseline without task-specific policy training or fine-tuning. Real-world experiments demonstrate accurate long-horizon tracking, reducing RMSE by 44.0% on the longest task. In obstacle avoidance, BM2PC achieves comparable performance to existing multimodal MPC methods while reducing planning time by 29% to 66%. These results demonstrate accurate dynamic control and efficient multimodal planning within a unified MPC framework. The core implementation of BM2PC and supplementary videos are available at https://github.com/Longyouyuan/BM2PC.

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