According to WHO statistics for 2018, there are 1.2 million cases and 700,000 deaths from breast cancer (BC) each year, making it the second-highest cause of mortality for women globally. In recent years, advances in artificial (AI) intelligence and machine (ML) learning have shown incredible potential in increasing the accuracy and efficiency of BC diagnosis. This research describes an intelligent BC image analysis system that leverages the capabilities of transfer learning (TLs) with ensemble stacking ML models. As part of this research, we created a model for analyzing ultrasound BC images using cutting-edge TL models such as Inception V3, VGG-19, and VGG-16. We have implemented stacking of ensemble ML models, including MLP (Multi-Layer Perceptron) with different architectures (10 10, 20 20, and 30 30) and Support Vector Machines (SVM) with RBF and Polynomial kernels. We analyzed the effectiveness of the proposed system in performance parameters (accuracy (CA), sensitivity, specificity, and AUC). Compared to the results with existing BC diagnostic systems, the proposed method (Inception V3 + Staking) is superior, with performance parameters 0.947 of AUC and 0.858 of CA values. The proposed BCUI analysis system consists of data collection, pre-processing, transfer learning, ensemble stacking of ML models, and performance evaluation, with comparative analysis demonstrating its superiority over existing methods.