Detecting and classifying lesions in breast ultrasound images is a promising application of artificial intelligence (AI) for reducing the burden of cancer in regions with limited access to mammography. Such AI systems are more likely to be useful in a clinical setting if their predictions can be explained to a radiologist. This work proposes an explainable AI model that provides interpretable predictions using a standard lexicon from the American College of Radiology's Breast Imaging and Reporting Data System (BI-RADS). The model is a deep neural network featuring a concept bottleneck layer in which known BI-RADS features are predicted before making a final cancer classification. This enables radiologists to easily review the predictions of the AI system and potentially fix errors in real time by modifying the concept predictions. In experiments, a model is developed on 8,854 images from 994 women with expert annotations and histological cancer labels. The model outperforms state-of-the-art lesion detection frameworks with 48.9 average precision on the held-out testing set, and for cancer classification, concept intervention is shown to increase performance from 0.876 to 0.885 area under the receiver operating characteristic curve.