Cloud platforms now host continuously changing data pipelines, model-serving systems, API gateways, and compliance-sensitive analytics. Manual governance processes cannot inspect every telemetry stream, configuration change, data movement, and policy exception at the pace of elastic infrastructure. This paper presents Policy-Bounded Agentic Cloud Governance (PACG), a control-plane architecture in which specialized AI agents propose operational actions but cannot execute them without formal policy checks, provenance capture, and staged actuation. PACG separates observation, reasoning, verification, execution, and audit functions so that agentic automation improves responsiveness without weakening accountability. A prototype evaluation across batch analytics, streaming ingestion, and model-serving workflows shows that the approach reduces mean recovery time by 39.8%, reduces unresolved policy drift by 34.6%, and lowers manual intervention events by 62.5% relative to static cloud operations, while keeping p95 actuation latency below 5.4%. The results suggest that the next phase of cloud governance will be neither fully manual nor fully autonomous, but a bounded collaboration among declarative policy, operational telemetry, and auditable agents.