Intraoperative bleeding in laparoscopic surgery causes rapid obscuration of the operative field to hinder the surgical process. Intelligent detection of bleeding regions can quantify the blood loss to assist decision-making, while locating the bleeding point helps surgeons quickly identify the source of bleeding and achieve hemostasis in time. In this study, we first construct a real-world surgical bleeding detection dataset, named SurgBlood, comprising 5,330 frames from 95 surgical video clips with bleeding region and point annotations. Accordingly, we develop a dual-task synergistic online detector called BlooDet, designed to perform simultaneous detection of bleeding regions and points in surgical videos. Our framework embraces a dual-branch bidirectional guidance design based on Segment Anything Model 2 (SAM 2). The mask branch detects bleeding regions through adaptive edge and point prompt embeddings, while the point branch leverages mask memory to induce bleeding point memory modeling and captures the direction of bleed point movement through inter-frame optical flow. By interactive guidance and prompts, the two branches explore potential spatial-temporal relationships while leveraging memory modeling from previous frames to infer the current bleeding condition. Extensive experiments demonstrate that our approach outperforms other counterparts on SurgBlood in both bleeding region and point detection tasks, e.g., achieving 64.88% IoU for bleeding region detection and 83.69% PCK-10% for bleeding point detection.