Breast cancer is one of the most common types of cancer and is the leading cause of cancer-related death. Diagnosis of breast cancer is based on the evaluation of pathology slides. In the era of digital pathology, these slides can be converted into digital whole slide images (WSIs) for further analysis. However, due to their sheer size, digital WSIs diagnoses are time consuming and challenging. In this study, we present a lightweight architecture that consists of a bilinear structure and MobileNet-V3 network, bilinear MobileNet-V3 (BM-Net), to analyze breast cancer WSIs. We utilized the WSI dataset from the ICIAR2018 Grand Challenge on Breast Cancer Histology Images (BACH) competition, which contains four classes: normal, benign, in situ carcinoma, and invasive carcinoma. We adopted data augmentation techniques to increase diversity and utilized focal loss to remove class imbalance. We achieved high performance, with 0.88 accuracy in patch classification and an average 0.71 score, which surpassed state-of-the-art models. Our BM-Net shows great potential in detecting cancer in WSIs and is a promising clinical tool.