Deep learning is advancing EEG processing for automated epileptic seizure detection and onset zone localization, yet its performance relies heavily on high-quality annotated training data. However, scalp EEG is susceptible to high noise levels, which in turn leads to imprecise annotations of the seizure timing and characteristics. This "label noise" presents a significant challenge in model training and generalization. In this paper, we introduce Bayesian UncertaiNty-aware Deep Learning (BUNDL), a novel algorithm that informs a deep learning model of label ambiguities, thereby enhancing the robustness of seizure detection systems. By integrating domain knowledge into an underlying Bayesian framework, we derive a novel KL-divergence-based loss function that capitalizes on uncertainty to better learn seizure characteristics from scalp EEG. Thus, BUNDL offers a straightforward and model-agnostic method for training deep neural networks with noisy training labels that does not add any parameters to existing architectures. Additionally, we explore the impact of improved detection system on the task of automated onset zone localization. We validate BUNDL using a comprehensive simulated EEG dataset and two publicly available datasets collected by Temple University Hospital (TUH) and Boston Children's Hospital (CHB-MIT). Results show that BUNDL consistently identifies noisy labels and improves the robustness of three base models under various label noise conditions. We also evaluate cross-site generalizability and quantify computational cost of all methods. Ultimately, BUNDL presents as a reliable method that can be seamlessly integrated with existing deep models used in clinical practice, enabling the training of trustworthy models for epilepsy evaluation.