This paper introduces a conversational interface system that enables participatory design of differentially private AI systems in public sector applications. Addressing the challenge of balancing mathematical privacy guarantees with democratic accountability, we propose three key contributions: (1) an adaptive $\epsilon$-selection protocol leveraging TOPSIS multi-criteria decision analysis to align citizen preferences with differential privacy (DP) parameters, (2) an explainable noise-injection framework featuring real-time Mean Absolute Error (MAE) visualizations and GPT-4-powered impact analysis, and (3) an integrated legal-compliance mechanism that dynamically modulates privacy budgets based on evolving regulatory constraints. Our results advance participatory AI practices by demonstrating how conversational interfaces can enhance public engagement in algorithmic privacy mechanisms, ensuring that privacy-preserving AI in public sector governance remains both mathematically robust and democratically accountable.