Public institutions seldom document the informal, undocumented processes that shape everyday work. As institutions digitize and modernize, such tacit knowledge is easily lost, particularly amid demographic change and limited process modeling expertise. To address this problem, we present Process Copilot, a generative AI system that converts natural language process descriptions into BPMN 2.0 models using large language models (LLMs). To improve the quality and reliability of generated process models, we incorporate domain-specific ontologies into the prompting process. We evaluate two prompting strategies, with and without ontologies, across ten real-world processes, using syntactic and structural similarity metrics alongside stability analysis based on output variance. Results indicate that ontology integration enhances semantic and structural performance, though at the cost of stability.