Ensuring access to medicines remains a persistent challenge in modern healthcare systems, particularly for high-cost drugs, where inadequate budgets or poor logistical planning can result in shortages or excessive stockpiling. To address this issue, this study explores the use of Bayesian-based forecasting models to predict demand and improve the efficiency, equity, and fairness of medicine distribution. A four-year monthly dataset of hospital consumption, enhanced with public cost data, was analyzed to pinpoint the most economically significant medicines. Leveraging the MLOps methodology, three models—Prophet, XGBoost, and SARIMAX—were developed, automated, and validated. Each model was fine-tuned using Bayesian hyperparameter optimization and assessed through cross-validation, with performance measured by MAPE, RMSE, and MAE. The findings indicate that Prophet performs best in relative accuracy for trend detection and smooth seasonality, XGBoost handles sudden fluctuations more effectively in absolute terms, and SARIMAX provides robust modeling of recurring cycles.