Recent advances in deep learning have led to a paradigm shift in reversible steganography. A fundamental pillar of reversible steganography is predictive modelling which can be realised via deep neural networks. However, non-trivial errors exist in inferences about some out-of-distribution and noisy data. In view of this issue, we propose to consider uncertainty in predictive models based upon a theoretical framework of Bayesian deep learning. Bayesian neural networks can be regarded as self-aware machinery; that is, a machine that knows its own limitations. To quantify uncertainty, we approximate the posterior predictive distribution through Monte Carlo sampling with stochastic forward passes. We further show that predictive uncertainty can be disentangled into aleatoric and epistemic uncertainties and these quantities can be learnt in an unsupervised manner. Experimental results demonstrate an improvement delivered by Bayesian uncertainty analysis upon steganographic capacity-distortion performance.