The mental well-being of graduate students is an increasing concern, yet the adoption of scalable support remains uneven. Artificial intelligence-powered cognitive behavioral therapy chatbots (AI-CBT) offer low barrier help, but little is known about how Chinese postgraduates perceive and use them. This qualitative study explored perceptions and experiences of AI-CBT chatbots among ten Chinese graduate students recruited through social media. Semi-structured Zoom interviews were conducted and analyzed using reflexive thematic analysis, with the Health Belief Model (HBM) and the Theory of Planned Behavior (TPB) as sensitizing frameworks. The findings indicate a cautious openness to AI-CBT chatbots: perceived usefulness and 24/7 access supported favorable attitudes, while data privacy, emotional safety, and uncertainty about `fit' for complex problems restricted the intention to use. Social norms (e.g., stigma and peer views) and perceived control (digital literacy, language quality) further shaped adoption. The study offers context-specific information to guide the culturally sensitive design, communication, and deployment of AI mental well-being tools for student populations in China and outlines the design implications around transparency, safeguards, and graduated care pathways.