Grocery recommendation is an important recommendation use-case, which aims to predict which items a user might choose to buy in the future, based on their shopping history. However, existing methods only represent each user and item by single deterministic points in a low-dimensional continuous space. In addition, most of these methods are trained by maximizing the co-occurrence likelihood with a simple Skip-gram-based formulation, which limits the expressive ability of their embeddings and the resulting recommendation performance. In this paper, we propose the Variational Bayesian Context-Aware Representation (VBCAR) model for grocery recommendation, which is a novel variational Bayesian model that learns the user and item latent vectors by leveraging basket context information from past user-item interactions. We train our VBCAR model based on the Bayesian Skip-gram framework coupled with the amortized variational inference so that it can learn more expressive latent representations that integrate both the non-linearity and Bayesian behaviour. Experiments conducted on a large real-world grocery recommendation dataset show that our proposed VBCAR model can significantly outperform existing state-of-the-art grocery recommendation methods.