Estimating depth from endoscopic images is a pre-requisite for a wide set of AI-assisted technologies, namely accurate localization, measurement of tumors, or identification of non-inspected areas. As the domain specificity of colonoscopies -a deformable low-texture environment with fluids, poor lighting conditions and abrupt sensor motions-pose challenges to multi-view approaches, single-view depth learning stands out as a promising line of research. In this paper, we explore for the first time Bayesian deep networks for single-view depth estimation in colonoscopies. Their uncertainty quantification offers great potential for such a critical application area. Our specific contribution is two-fold: 1) an exhaustive analysis of Bayesian deep networks for depth estimation in three different datasets, highlighting challenges and conclusions regarding synthetic-to-real domain changes and supervised vs. self-supervised methods; and 2) a novel teacherstudent approach to deep depth learning that takes into account the teacher uncertainty.