The premise of this paper is that compliance with Trustworthy AI governance best practices and regulatory frameworks is an inherently fragmented process spanning across diverse organizational units, external stakeholders, and systems of record, resulting in process uncertainties and in compliance gaps that may expose organizations to reputational and regulatory risks. Moreover, there are complexities associated with meeting the specific dimensions of Trustworthy AI best practices such as data governance, conformance testing, quality assurance of AI model behaviors, transparency, accountability, and confidentiality requirements. These processes involve multiple steps, hand-offs, re-works, and human-in-the-loop oversight. In this paper, we demonstrate that process mining can provide a useful framework for gaining fact-based visibility to AI compliance process execution, surfacing compliance bottlenecks, and providing for an automated approach to analyze, remediate and monitor uncertainty in AI regulatory compliance processes.