Trained DNN models are increasingly adopted as integral parts of software systems. However, they are often over-confident, especially in practical operation domains where slight divergence from their training data almost always exists. To minimize the loss due to inaccurate confidence, operational calibration, i.e., calibrating the confidence function of a DNN classifier against its operation domain, becomes a necessary debugging step in the engineering of the whole system. Operational calibration is difficult considering the limited budget of labeling operation data and the weak interpretability of DNN models. We propose a Bayesian approach to operational calibration that gradually corrects the confidence given by the model under calibration with a small number of labeled operational data deliberately selected from a larger set of unlabeled operational data. Exploiting the locality of the learned representation of the DNN model and modeling the calibration as Gaussian Process Regression, the approach achieves impressive efficacy and efficiency. Comprehensive experiments with various practical data sets and DNN models show that it significantly outperformed alternative methods, and in some difficult tasks it eliminated about 71% to 97% high-confidence errors with only about 10% of the minimal amount of labeled operation data needed for practical learning techniques to barely work.