Optical Coherence Tomography (OCT) provides valuable insights in ophthalmology, cardiology, and neurology due to high-resolution, cross-sectional images of the retina. One critical task for ophthalmologists using OCT is delineation of retinal layers within scans. This process is time-consuming and prone to human bias, affecting the accuracy and reliability of diagnoses. Previous efforts to automate delineation using deep learning face challenges in uptake from clinicians and statisticians due to the absence of uncertainty estimation, leading to "confidently wrong" models via hallucinations. In this study, we address these challenges by applying Bayesian convolutional neural networks (BCNNs) to segment an openly available OCT imaging dataset containing 35 human retina OCTs split between healthy controls and patients with multiple sclerosis. Our findings demonstrate that Bayesian models can be used to provide uncertainty maps of the segmentation, which can further be used to identify highly uncertain samples that exhibit recording artefacts such as noise or miscalibration at inference time. Our method also allows for uncertainty-estimation for important secondary measurements such as layer thicknesses, that are medically relevant for patients. We show that these features come in addition to greater performance compared to similar work over all delineations; with an overall Dice score of 95.65%. Our work brings greater clinical applicability, statistical robustness, and performance to retinal OCT segmentation.