Homodyned K-distribution (HK-distribution) parameter estimation in quantitative ultrasound (QUS) has been recently addressed using Bayesian Neural Networks (BNNs). BNNs have been shown to significantly reduce computational time in speckle statistics-based QUS without compromising accuracy and precision. Additionally, they provide estimates of feature uncertainty, which can guide the clinician's trust in the reported feature value. The total predictive uncertainty in Bayesian modeling can be decomposed into epistemic (uncertainty over the model parameters) and aleatoric (uncertainty inherent in the data) components. By decomposing the predictive uncertainty, we can gain insights into the factors contributing to the total uncertainty. In this study, we propose a method to compute epistemic and aleatoric uncertainties for HK-distribution parameters ($α$ and $k$) estimated by a BNN, in both simulation and experimental data. In addition, we investigate the relationship between the prediction error and both uncertainties, shedding light on the interplay between these uncertainties and HK parameters errors.