Wind speed forecasting can serve a wide spectrum of purposes, including scheduling of a power system and dynamic control of structures. A lot of models are widely used to forecast wind speed, consisting of deterministic models (e.g., physical models, statistical models, and artificial intelligence models) and probabilistic models (e.g., Bayesian model). The wind speed has the characteristics of random, nonlinear, and uncertainty, which highlights the importance of using Bayesian model to predict the wind speed. In this study, a Bayesian emulator with Gaussian process prior is adopted for probabilistic forecast of wind speed. The present Bayesian emulator approach not only maintains the data-driven property which guarantees its high flexibility in modeling the complexity of the target system but also allows for the efficient, probabilistic evaluation of the wind speed in terms of the predictive mean and variance. Nevertheless, the modeling performance of the Bayesian emulator directly depends on the selected covariance function. The influence of different types of covariance functions, which include squared-exponential (SE) covariance function, Matern (MA) covariance function, periodic (PE) covariance function, and composite covariance function, on forecasting performance of the wind speed is studied. One-month wind monitoring data collected by structural health monitoring (SHM) system installed on Jiubao bridge are employed to demonstrate the effectiveness of Bayesian emulator for forecasting the wind speed.