Spatio-temporal data often exhibit complex dependence structures and skewness, which makes their modeling with classical frameworks, such as Gaussian random fields, either computationally expensive or overly restrictive. In this paper, we introduce a novel Bayesian Neural Field framework for modeling skewed spatio-temporal processes. The proposed approach incorporates spatial and temporal coordinates, along with explanatory variables and prior distributions, allowing flexible representation of dependence and skewness, as well as prediction at new locations and at unseen time points. Parameter inference is performed using variational inference, which offers both computational efficiency and the ability to quantify uncertainty. Simulation results demonstrate that the proposed framework achieves higher accuracy and faster computation compared to standard Monte Carlo methods.