Robotic manipulation of deformable materials is a challenging task that often requires realtime visual feedback. This is especially true for deformable linear objects (DLOs) or "rods", whose slender and flexible structures make proper tracking and detection nontrivial. To address this challenge, we present mBEST, a robust algorithm for the realtime detection of DLOs that is capable of producing an ordered pixel sequence of each DLO's centerline along with segmentation masks. Our algorithm obtains a binary mask of the DLOs and then thins it to produce a skeleton pixel representation. After refining the skeleton to ensure topological correctness, the pixels are traversed to generate paths along each unique DLO. At the core of our algorithm, we postulate that intersections can be robustly handled by choosing the combination of paths that minimizes the cumulative bending energy of the DLO(s). We show that this simple and intuitive formulation outperforms the state-of-the-art methods for detecting DLOs with large numbers of sporadic crossings ranging from curvatures with high variance to nearly-parallel configurations. Furthermore, our method achieves a significant performance improvement of approximately 50% faster runtime and better scaling over the state of the art.