The availability of accurate day-ahead energy prices forecasts is crucial to achieve a successful participation to liberalized electricity markets. Moreover, forecasting systems providing prediction intervals and densities (i.e. probabilistic forecasting) are fundamental to enable enhanced bidding and planning strategies considering uncertainty explicitly. Nonetheless, the vast majority of available approaches focus on point forecast. Therefore, we propose a novel methodology for probabilistic energy price forecast based on Bayesian deep learning techniques. A specific training method has been deployed to guarantee scalability to complex network architectures. Moreover, we developed a model originally supporting heteroscedasticity, thus avoiding the common homoscedastic assumption with related preprocessing effort. Experiments have been performed on two day ahead markets characterized by different behaviors. Then, we demonstrated the capability of the proposed method to achieve robust performances in out-of-sample conditions while providing forecast uncertainty indications.