Rapid urbanization in the Gulf Cooperation Council (GCC) has rendered traditional traffic management systems inadequate, creating significant economic and environmental costs. This paper presents a strategic framework for the digital transformation of urban mobility, leveraging machine learning (ML) as a core driver of public sector innovation. Using Bahrain's Saar Interchange as a real-world case study, this research develops and validates a multi-faceted ML system in MATLAB. The framework integrates three critical components: a time-series model for traffic volume forecasting, a logistic regression model for proactive accident risk prediction, and a Monte Carlo simulation model for evaluating infrastructure scenarios pre-implementation. The models demonstrate high accuracy and practical utility, even with limited data, providing a robust, cost-effective toolkit for data-driven decision-making. The findings confirm that ML can transform reactive traffic management into a proactive, predictive, and optimized system. This research offers an actionable and scalable blueprint for Bahrain and other GCC nations to advance their smart city ambitions, aligning with national development goals like Bahrain's Vision 2030 and contributing a valuable model to the global discourse on intelligent transportation systems.