Credit card fraud poses a significant threat to financial institutions, causing financial losses and eroding customer trust. Detecting fraud requires accurate, efficient solutions, but imbalanced data where legitimate transactions far outnumber fraudulent ones complicates the challenge. To address this, we propose an enhanced fraud detection framework combining data-level and algorithmic-level approaches. At the data level, we use the Synthetic Minority Over-sampling Technique (SMOTE) to generate synthetic minority class samples. At the algorithmic level, we employ a Bayesian Neural Network (BNN), which provides robust predictions and quantifies uncertainty critical for high-stakes applications like fraud detection. The framework achieves 99.37% precision, minimizing false positives, and a 97.52% AUC, demonstrating its ability to distinguish between fraudulent and legitimate transactions. These results underscore the effectiveness of Bayesian Neural Networks in fraud detection, offering high precision and reliability. This improved system reduces disruptions, minimizes financial losses, and enhances trust, setting a new standard for applying machine learning to complex, imbalanced data challenges in critical business applications.