Learning from demonstrations (LfD) improves the exploration efficiency of a learning agent by incorporating demonstrations from experts. However, demonstration data can often come from multiple experts with conflicting goals, making it difficult to incorporate safely and effectively in online settings. We address this problem in the static and dynamic optimization settings by modelling the uncertainty in source and target task functions using normal-inverse-gamma priors, whose corresponding posteriors are, respectively, learned from demonstrations and target data using Bayesian neural networks with shared features. We use this learned belief to derive a quadratic programming problem whose solution yields a probability distribution over the expert models. Finally, we propose Bayesian Experience Reuse (BERS) to sample demonstrations in accordance with this distribution and reuse them directly in new tasks. We demonstrate the effectiveness of this approach for static optimization of smooth functions, and transfer learning in a high-dimensional supply chain problem with cost uncertainty.