The advancement in 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 pose new challenges to the network operational planning with underlying uncertainties. This paper proposes a novel Bayesian probabilistic technique for forecasting renewable power 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 pinball loss, reconstruction error, and other forecasting evaluation metrics. It is inferred from the numerical results that VAE-Bayesian BiLSTM outperforms other probabilistic deep learning methods in terms of forecasting accuracy and computational efficiency for different sizes of the dataset.