Exploring the mechanism of hysteresis dynamics may facilitate the analysis and controller design to alleviate detrimental effects. Conventional models, such as the Bouc-Wen and Preisach models consist of complicated nonlinear structures, limiting the applications of hysteresis systems for high-speed and high-precision positioning, detection, execution, and other operations. In this article, a Bayesian Koopman (B-Koopman) learning algorithm is therefore developed to characterize hysteresis dynamics. Essentially, the proposed scheme establishes a simplified linear representation with time delay for hysteresis dynamics, where the properties of the original nonlinear system are preserved. Furthermore, model parameters are optimized via sparse Bayesian learning together with an iterative strategy, which simplifies the identification procedure and reduces modeling errors. Extensive experimental results on piezoelectric positioning are elaborated to substantiate the effectiveness and superiority of the proposed B-Koopman algorithm for learning hysteresis dynamics.