This study developed a model to understand the communication dynamics of generative artificial intelligence (GAI) bias cognition within a two-layer network comprising enterprise managers and ordinary employees. The model integrated the effects of communication between different levels and the impact of cognitive training. Using the next-generation matrix method, the study accurately calculated the propagation threshold, R0, that served as a crucial quantitative foundation for effective governance. Specifically, when R0<1, deviant cognition tended to disappear spontaneously, whereas when R0>1, a risk of biased cognition spreading existed. Additionally, the study compared and evaluated two intervention strategies through numerical simulations, providing a comprehensive analysis of the mechanisms that drove the generation and dissemination of deviant cognition within enterprises, supported by case studies.