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Screening mammograms is the gold standard for detecting breast cancer early. While a good amount of work has been performed on mammography image classification, especially with deep neural networks, there has not been much exploration into the confidence or uncertainty measurement of the classification. In this paper, we propose a confidence measure-based evaluation metric for breast cancer screening. We propose a modular network architecture, where a traditional neural network is used as a feature extractor with transfer learning, followed by a simple Bayesian neural network. Utilizing a two-stage approach helps reducing the computational complexity, making the proposed framework attractive for wider deployment. We show that by providing the medical practitioners with a tool to tune two hyperparameters of the Bayesian neural network, namely, fraction of sampled number of networks and minimum probability, the framework can be adapted as needed by the domain expert. Finally, we argue that instead of just a single number such as accuracy, a tuple (accuracy, coverage, sampled number of networks, and minimum probability) can be utilized as an evaluation metric of our framework. We provide experimental results on the CBIS-DDSM dataset, where we show the trends in accuracy-coverage tradeoff while tuning the two hyperparameters. We also show that our confidence tuning results in increased accuracy with a reduced set of images with high confidence when compared to the baseline transfer learning. To make the proposed framework readily deployable, we provide (anonymized) source code with reproducible results at https://git.io/JvRqE.