As generative artificial intelligence (AI) systems become increasingly integrated into education, professional and social domains, user trust emerges as a critical factor influencing their adoption and continued use. This study examines the multifaceted nature of trust in Generative AI, focusing on the roles of perceived competences, usefulness and privacy concerns in shaping user satisfaction. Drawing on trust theory, a conceptual framework was developed and empirically tested using survey data from 354 UK-based users of Generative AI platforms. Structural equation modelling revealed that perceived competence, benevolence, integrity, usefulness and ease of use significantly influence trust, which in turn drives user satisfaction. Conversely, privacy and security concerns were found to negatively impact trust. The study highlights the need for AI developers and policymakers to ensure transparency, ethical design and privacy safeguards to enhance user trust and promote responsible AI adoption.