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This work proposes a comprehensively progressive Bayesian neural network for robust continual learning of a sequence of tasks. A Bayesian neural network is progressively pruned and grown such that there are sufficient network resources to represent a sequence of tasks, while the network does not explode. It starts with the contention that similar tasks should have the same number of total network resources, to ensure fair representation of all tasks in a continual learning scenario. Thus, as the data for new task streams in, sufficient neurons are added to the network such that the total number of neurons in each layer of the network, including the shared representations with previous tasks and individual task related representation, are equal for all tasks. The weights that are redundant at the end of training each task are also pruned through re-initialization, in order to be efficiently utilized in the subsequent task. Thus, the network grows progressively, but ensures effective utilization of network resources. We refer to our proposed method as 'Robust Continual Learning through a Comprehensively Progressive Bayesian Neural Network (RCL-CPB)' and evaluate the proposed approach on the MNIST data set, under three different continual learning scenarios. Further to this, we evaluate the performance of RCL-CPB on a homogeneous sequence of tasks using split CIFAR100 (20 tasks of 5 classes each), and a heterogeneous sequence of tasks using MNIST, SVHN and CIFAR10 data sets. The demonstrations and the performance results show that the proposed strategies for progressive BNN enable robust continual learning.