One of the challenges with model-based control of stochastic dynamical systems is that the state transition dynamics are involved, making it difficult and inefficient to make good-quality predictions of the states. Moreover, there are not many representational models for the majority of autonomous systems, as it is not easy to build a compact model that captures all the subtleties and uncertainties in the system dynamics. In this work, we present a hierarchical Bayesian linear regression model with local features to learn the dynamics of such systems. The model is hierarchical since we consider non-stationary priors for the model parameters which increases its flexibility. To solve the maximum likelihood (ML) estimation problem for this hierarchical model, we use the variational expectation maximization (EM) algorithm, and enhance the procedure by introducing hidden target variables. The algorithm is guaranteed to converge to the optimal log-likelihood values under certain reasonable assumptions. It also yields parsimonious model structures, and consistently provides fast and accurate predictions for all our examples, including two illustrative systems and a challenging micro-robotic system, involving large training and test sets. These results demonstrate the effectiveness of the method in approximating stochastic dynamics, which make it suitable for future use in a paradigm, such as model-based reinforcement learning, to compute optimal control policies in real time.