In recent years, there has been increasing amount of interest around meta reinforcement learning methods for traffic signal control, which have achieved better performance compared with traditional control methods. However, previous methods lack robustness in adaptation and stability in training process in complex situations, which largely limits its application in real-world traffic signal control. In this paper, we propose a novel value-based Bayesian meta-reinforcement learning framework BM-DQN to robustly speed up the learning process in new scenarios by utilizing well-trained prior knowledge learned from existing scenarios. This framework is based on our proposed fast-adaptation variation to Gradient-EM Bayesian Meta-learning and the fast-update advantage of DQN, which allows for fast adaptation to new scenarios with continual learning ability and robustness to uncertainty. The experiments on restricted 2D navigation and traffic signal control show that our proposed framework adapts more quickly and robustly in new scenarios than previous methods, and specifically, much better continual learning ability in heterogeneous scenarios.