This paper introduces a novel Hybrid Visual Servoing (HVS) approach for controlling tendon-driven continuum robots (TDCRs). The HVS system combines Image-Based Visual Servoing (IBVS) with Deep Learning-Based Visual Servoing (DLBVS) to overcome the limitations of each method and improve overall performance. IBVS offers higher accuracy and faster convergence in feature-rich environments, while DLBVS enhances robustness against disturbances and offers a larger workspace. By enabling smooth transitions between IBVS and DLBVS, the proposed HVS ensures effective control in dynamic, unstructured environments. The effectiveness of this approach is validated through simulations and real-world experiments, demonstrating that HVS achieves reduced iteration time, faster convergence, lower final error, and smoother performance compared to DLBVS alone, while maintaining DLBVS's robustness in challenging conditions such as occlusions, lighting changes, actuator noise, and physical impacts.