This paper presents a Bayesian framework for unsupervised domain adaptation of Probabilistic Linear Discriminant Analysis (PLDA). By interpreting class labels as latent random variables, Variational Bayes (VB) is used to derive a maximum a posterior (MAP) solution of the adapted PLDA model when labels are missing, referred to as VB-MAP. The VB solution iteratively infers class labels and updates PLDA hyperparameters, offering a systematic framework for dealing with unlabeled data. While presented as a general solution, this paper includes experimental results for domain adaptation in speaker verification. VBMAP estimation is applied to the 2016 and 2018 NIST Speaker Recognition Evaluations (SREs), both of which included small and unlabeled in-domain data sets, and is shown to provide performance improvements over a variety of state-of-the-art domain adaptation methods. Additionally, VB-MAP estimation is used to train a fully unsupervised PLDA model, suffering only minor performance degradation relative to conventional supervised training, offering promise for training PLDA models when no relevant labeled data exists.