In this work, we aim to establish a Bayesian adaptive learning framework by focusing on estimating latent variables in deep neural network (DNN) models. Latent variables indeed encode both transferable distributional information and structural relationships. Thus the distributions of the source latent variables (prior) can be combined with the knowledge learned from the target data (likelihood) to yield the distributions of the target latent variables (posterior) with the goal of addressing acoustic mismatches between training and testing conditions. The prior knowledge transfer is accomplished through Variational Bayes (VB). In addition, we also investigate Maximum a Posteriori (MAP) based Bayesian adaptation. Experimental results on device adaptation in acoustic scene classification show that our proposed approaches can obtain good improvements on target devices, and consistently outperforms other cut-edging algorithms.