Bronchoscopic navigation plays an essential role in helping surgeons perceive the location of bronchoscopy and providing guidance for minimally invasive procedures. Vision-based navigation methods, particularly visual SLAM, have gained popularity due to their convenience and simple configuration. However, the poor texture and low contrast of bronchoscopic images may break down the conventional visual SLAM-based navigation system due to insufficient feature matches and a lack of reliable keypoints for pose estimation. This work proposes a new dense depth-supervised visual SLAM framework to draw benefits from the recent success of detector-free matchers and monocular depth estimation to maintain continuous and stable tracking of autonomous bronchoscopic navigation. Specifically, our framework first employs a dense detector-free feature-matching model to obtain more widely distributed matching pairs between low-quality bronchoscopic images. Moreover, we train an accurate monocular dense depth estimation model and integrate it into visual SLAM to obtain more 3D points for camera pose estimation via Perspective-n-Point (PnP), thereby improving tracking performance. We collected CT and bronchoscopic videos from the hospital for evaluation. The experimental results demonstrate that our proposed framework achieves more accurate and continuous bronchoscopic navigation results compared to the state-of-the-art visual SLAM methods.