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Personalized learning is a promising educational approach that aims to provide high-quality personalized services for each student with minimum demands for practice data. The key to achieving that lies in the cognitive diagnosis task, which estimates the cognitive state of the student through his/her logged data of doing practice quizzes. Nevertheless, in the personalized learning scenario, existing cognitive diagnosis models suffer from the inability to (1) quickly adapt to new students using a small amount of data, and (2) measure the reliability of the diagnosis result to avoid improper services that mismatch the student's actual state. In this paper, we propose a general Bayesian mETA-learned Cognitive Diagnosis framework (BETA-CD), which addresses the two challenges by prior knowledge exploitation and model uncertainty quantification, respectively. Specifically, we firstly introduce Bayesian hierarchical modeling to associate each student's cognitive state with a shared prior distribution encoding prior knowledge and a personal posterior distribution indicating model uncertainty. Furthermore, we formulate a meta-learning objective to automatically exploit prior knowledge from historical students, and efficiently solve it with a gradient-based variational inference method. The code will be publicly available at https://github.com/AyiStar/pyat.