Breast ultrasound is a useful and rapid diagnostic tool for the early detection of breast cancer. Artificial intelligence-supported computer-aided decision systems, which assist expert radiologists and clinicians, provide reliable and rapid results. Deep learning methods and techniques are widely used in the field of health for early diagnosis, abnormality detection, and disease diagnosis. Therefore, in this study, a deep ensemble learning model based on Dirichlet distribution using pre-trained transfer learning models for breast cancer classification from ultrasound images is proposed. In the study, experiments were conducted using the Breast Ultrasound Images Dataset (BUSI). The dataset, which had an imbalanced class structure, was balanced using data augmentation techniques. DenseNet201, InceptionV3, VGG16, and ResNet152 models were used for transfer learning with fivefold cross-validation. Statistical analyses, including the ANOVA test and Tukey HSD test, were applied to evaluate the model's performance and ensure the reliability of the results. Additionally, Grad-CAM (Gradient-weighted Class Activation Mapping) was used for explainable AI (XAI), providing visual explanations of the deep learning model's decision-making process. The spaced repetition method, commonly used to improve the success of learners in educational sciences, was adapted to artificial intelligence in this study. The results of training with transfer learning models were used as input for further training, and spaced repetition was applied using previously learned information. The use of the spaced repetition method led to increased model success and reduced learning times. The weights obtained from the trained models were input into an ensemble learning system based on Dirichlet distribution with different variations. The proposed model achieved 99.60% validation accuracy on the dataset, demonstrating its effectiveness in breast cancer classification.