The advancement of distributed generation technologies in modern power systems has led to a widespread integration of renewable power generation at customer side. However, the intermittent nature of renewable energy poses new challenges to the network operational planning with underlying uncertainties. This paper proposes a novel Bayesian probabilistic technique for forecasting renewable solar generation by addressing data and model uncertainties by integrating bidirectional long short-term memory (BiLSTM) neural networks while compressing the weight parameters using variational autoencoder (VAE). Existing Bayesian deep learning methods suffer from high computational complexities as they require to draw a large number of samples from weight parameters expressed in the form of probability distributions. The proposed method can deal with uncertainty present in model and data in a more computationally efficient manner by reducing the dimensionality of model parameters. The proposed method is evaluated using quantile loss, reconstruction error, and deterministic forecasting evaluation metrics such as root-mean square error. It is inferred from the numerical results that VAE-Bayesian BiLSTM outperforms other probabilistic and deterministic deep learning methods for solar power forecasting in terms of accuracy and computational efficiency for different sizes of the dataset.