Bayesian Neural Networks (BayNNs) naturally provide uncertainty in their predictions, making them a suitable choice in safety-critical applications. Additionally, their realization using memristor-based in-memory computing (IMC) architectures enables them for resource-constrained edge applications. In addition to predictive uncertainty, however, the ability to be inherently robust to noise in computation is also essential to ensure functional safety. In particular, memristor-based IMCs are susceptible to various sources of non-idealities such as manufacturing and runtime variations, drift, and failure, which can significantly reduce inference accuracy. In this paper, we propose a method to inherently enhance the robustness and inference accuracy of BayNNs deployed in IMC architectures. To achieve this, we introduce a novel normalization layer combined with stochastic affine transformations. Empirical results in various benchmark datasets show a graceful degradation in inference accuracy, with an improvement of up to $58.11\%$.