As autonomous systems increasingly rely on Deep Neural Networks (DNN) to implement the navigation pipeline functions, uncertainty estimation methods have become paramount for estimating confidence in DNN predictions. Bayesian Deep Learning (BDL) offers a principled approach to model uncertainties in DNNs. However, in DNN-based systems, not all the components use uncertainty estimation methods and typically ignore the uncertainty propagation between them. This paper provides a method that considers the uncertainty and the interaction between BDL components to capture the overall system uncertainty. We study the effect of uncertainty propagation in a BDL-based system for autonomous aerial navigation. Experiments show that our approach allows us to capture useful uncertainty estimates while slightly improving the system's performance in its final task. In addition, we discuss the benefits, challenges, and implications of adopting BDL to build dependable autonomous systems.