The widespread adoption of machine learning necessitates robust privacy protection alongside algorithmic resilience. While Local Differential Privacy (LDP) provides foundational guarantees, sophisticated adversaries with prior knowledge demand more nuanced Bayesian privacy notions, such as Maximum Bayesian Privacy (MBP) and Average Bayesian Privacy (ABP), first introduced by \cite{zhang2022no}. Concurrently, machine learning systems require inherent robustness against data perturbations and adversarial manipulations. This paper systematically investigates the intricate theoretical relationships among LDP, MBP, and ABP. Crucially, we bridge these privacy concepts with algorithmic robustness, particularly within the Probably Approximately Correct (PAC) learning framework. Our work demonstrates that privacy-preserving mechanisms inherently confer PAC robustness. We present key theoretical results, including the formalization of the established LDP-MBP relationship, novel bounds between MBP and ABP, and a proof demonstrating PAC robustness from MBP. Furthermore, we establish a novel theoretical relationship quantifying how privacy leakage directly influences an algorithm's input robustness. These results provide a unified theoretical framework for understanding and optimizing the privacy-robustness trade-off, paving the way for the development of more secure, trustworthy, and resilient machine learning systems.