Artificial Intelligence (AI) is driving ecological shifts and systemic reforms in education. As practitioners of educational reform, teachers' behavioral intention to experience and accept the effectiveness of AI technologies will affect the quality of educational change. From an educational ecology perspective, this study explores the impact of core elements within three dimensions--technologies, pedagogies, and cultures--on teachers' behavioral intention to use AI in an AI-enabled educational ecosystem (AI-e3) environment. The study uses a multi-level mediation model to analyze data of 4349 teachers from 189 primary and secondary schools from a western province of China. The results indicated that school-level dimensional elements, directly or indirectly, influenced teachers' behavioral intention to use AI, mediated by teacher-level dimensional elements. The findings are relevant to school administrators and policy makers, who should consider the key influences on teachers' behavioral intentions to use AI and promote the effective application of AI science for educational change.