Mean opinion score (MOS) is a bounded speech quality measure, ranging between 1 and 5. We propose using a Beta distribution to model the posterior of the bounded MOS for a given speech clip. We use a deep neural network (DNN), trained using a maximum-likelihood principle, providing the parameters of the posterior Beta distribution. A self-teacher learning setup is used to achieve robustness against the inherent challenge of training on a noisy dataset. The dataset noise comes from the subjective nature of the MOS labels, and only a handful of quality score ratings are provided for each speech clip. To compare with existing state-of-the-art methods, we use the mean of Beta posterior as a point estimate of the MOS. The proposed method shows competitive performance vis-a-vis several existing DNN-based methods that provide MOS point estimates, and an ablation study shows the importance of various components of the proposed method.