Recent research has proposed that Content Delivery Networks (CDNs) can use better bandwidth allocation to improve video streaming services through congested links. Because CDNs are usually not located at the bottleneck link, shared bottleneck (co-bottleneck) detection on the video servers is necessary for joint flow shaping and the Quality of Experience (QoE) improvements. However, co-bottleneck detection is challenging in such environments due to the large number of flows, possible network topologies, and traffic patterns. Current detectors fail to balance detection accuracy, speed and overhead, and suffer performance degradation in the scale of thousands of flows on each video server. We propose FlowBot, a novel model-based passive co-bottleneck detector designed for deployment on a video server. FlowBot uses Siamese model to learn flow representations, and combines the training procedure with its clustering algorithm to continue to provide strong performance with up to thousands of flows. Our evaluations show that FlowBot can achieve consistently high accuracy (over 70% F1 with around 90% precision) in most tested scenarios, while maintaining a short detection delay of 3 s and overhead similar to the fastest benchmark algorithms.