Upcoming experiments such as Hydrogen Epoch of Reionization Array (HERA) and Square Kilometre Array (SKA) are intended to measure the 21cm signal over a wide range of redshifts, representing an incredible opportunity in advancing our understanding about the nature of cosmic Reionization. At the same time these kind of experiments will present new challenges in processing the extensive amount of data generated, calling for the development of automated methods capable of precisely estimating physical parameters and their uncertainties. In this paper we employ Variational Inference, and in particular Bayesian Neural Networks, as an alternative to MCMC in 21 cm observations to report credible estimations for cosmological and astrophysical parameters and assess the correlations among them.