Fast machine learning-based surrogate models are trained to emulate slow, high-fidelity engineering simulation models to accelerate engineering design tasks. This introduces uncertainty as the surrogate is only an approximation of the original model. Bayesian methods can quantify that uncertainty, and deep learning models exist that follow the Bayesian paradigm. These models, namely Bayesian neural networks and Gaussian process models, enable us to give predictions together with an estimate of the model's uncertainty. As a result we can derive uncertainty-aware surrogate models that can automatically suspect unseen design samples that cause large emulation errors. For these samples, the high-fidelity model can be queried instead. This outlines how the Bayesian paradigm allows us to hybridize fast, but approximate, and slow, but accurate models. In this paper, we train two types of Bayesian models, dropout neural networks and stochastic variational Gaussian Process models, to emulate a complex high dimensional building energy performance simulation problem. The surrogate model processes 35 building design parameters (inputs) to estimate 12 different performance metrics (outputs). We benchmark both approaches, prove their accuracy to be competitive, and show that errors can be reduced by up to 30% when the 10% of samples with the highest uncertainty are transferred to the high-fidelity model.