In this work, we aim to enhance the system robustness of end-to-end automatic speech recognition (ASR) against adversarially-noisy speech examples. We focus on a rigorous and empirical "closed-model adversarial robustness" setting (e.g., on-device or cloud applications). The adversarial noise is only generated by closed-model optimization (e.g., evolutionary and zeroth-order estimation) without accessing gradient information of a targeted ASR model directly. We propose an advanced Bayesian neural network (BNN) based adversarial detector, which could model latent distributions against adaptive adversarial perturbation with divergence measurement. We further simulate deployment scenarios of RNN Transducer, Conformer, and wav2vec-2.0 based ASR systems with the proposed adversarial detection system. Leveraging the proposed BNN based detection system, we improve detection rate by +2.77 to +5.42% (relative +3.03 to +6.26%) and reduce the word error rate by 5.02 to 7.47% on LibriSpeech datasets compared to the current model enhancement methods against the adversarial speech examples.