© 2020, Springer Nature Switzerland AG. We present an original automated framework for estimating gestational age (GA) from fetal ultrasound head biometry plane images. A novelty of our approach is the use of a Bayesian Neural Network (BNN), which quantifies uncertainty of the estimated GA. Knowledge of estimated uncertainty is useful in clinical decision-making, and is especially important in ultrasound image analysis where image appearance and quality can naturally vary a lot. A further novelty of our approach is that the neural network is not provided with images pixel size, thus making it rely on anatomical appearance characteristics and not size. We train the network using 9,299 scans from the INTERGROWTH-21st[22] dataset ranging from weeks to weeks GA. We achieve average RMSE and MAE of 9.6 and 12.5 days respectively over the GA range. We explore the robustness of the BNN architecture to invalid input images by testing with (i) a different dataset derived from routine anomaly scanning and (ii) scans of a different fetal anatomy.