Given the underlying road network of an urban area, the problem of urban dynamics prediction aims to capture the patterns of urban dynamics and to forecast short-term urban traffic status continuously from the historical observations. This problem is of fundamental importance to urban traffic management, planning, and various business services. However, predicting urban dynamics is challenging due to the highly dynamic (i.e., varying across geographical locations and evolving over time) and uncertain (i.e., affected by unexpected factors) nature of urban traffic systems. Recent works adopt meta-learning approaches to capture irregular and rare patterns but make unrealistic assumptions such as single-domain uncertainties and explicit temporal task segmentation. In this paper, we solve the urban dynamics prediction problem from the Bayesian meta-learning perspective and propose a novel domain adaptable continuous meta-learning approach (DAC-ML) that does not require task segmentation. Trained on a sequence of spatial-temporal urban dynamics data, DAC-ML aims to detect and infer unobserved latent variations (from task and domain levels) and generalize well in a sequential prediction setting, where the underlying data generating process varies over time. Experimental results on three real-world datasets demonstrate that DAC-ML can outperform baselines in urban dynamics prediction, especially when obvious urban dynamics and temporal uncertainties are present.