Video bronchoscopy is routinely conducted for biopsies of lung tissue suspected for cancer, monitoring of COPD patients and clarification of acute respiratory problems at intensive care units. The navigation within complex bronchial trees is particularly challenging and physically demanding, requiring long-term experiences of physicians. This paper addresses the automatic segmentation of bronchial orifices in bronchoscopy videos. Deep learning-based approaches to this task are currently hampered due to the lack of readily-available ground truth segmentation data. Thus, we present a data-driven pipeline consisting of a k-means followed by a compact marker-based watershed algorithm which enables to generate airway instance segmentation maps from given depth images. In this way, these traditional algorithms serve as weak supervision for training a shallow CNN directly on RGB images solely based on a phantom dataset. We evaluate generalization capabilities of this model on two in-vivo datasets covering 250 frames on 21 different bronchoscopies. We demonstrate that its performance is comparable to those models being directly trained on in-vivo data, reaching an average error of 11 vs 5 pixels for the detected centers of the airway segmentation by an image resolution of 128x128. Our quantitative and qualitative results indicate that in the context of video bronchoscopy, phantom data and weak supervision using non-learning-based approaches enable to gain a semantic understanding of airway structures.