Convolutional neural networks have shown great potential in medical segmentation problems, such as braintumor segmentation. However, little consideration has been given to generative adversarial networks and uncertainty quantification over the output images. In this paper, we use the generative adversarial network to handle limited labeled images. We also quantify the modeling uncertainty by utilizing Bayesian active learning to reduce untoward outcomes. Bayesian active learning is dependent on selecting uncertain images using acquisition functions to increase accuracy. We introduce supervised acquisition functions based on distance functions between ground-truth and predicted images to quantify segmentation uncertainty. We evaluate the method by comparing it with the state-of-the-art methods based on Dice score, Hausdorff distance and sensitivity. We demonstrate that the proposed method achieves higher or comparable performance to state-of-the-art methods for brain tumor segmentation (on BraTS 2017, BraTS 2018 and BraTS 2019 datasets).