Gaussian process (GP) regression is one promising technique of constructing machine learning force fields with built-in uncertainty quantification, which can be used to monitor the quality of model predictions. A current limitation of existing GP force fields is that the prediction cost grows linearly with the size of the training data set, making accurate GP predictions slow. In this work, we exploit the special structure of the kernel function to construct a mapping of the trained Gaussian process model, including both forces and their uncertainty predictions, onto spline functions of low-dimensional structural features. This method is incorporated in the Bayesian active learning workflow for training of Bayesian force fields. To demonstrate the capabilities of this method, we construct a force field for stanene and perform large scale dynamics simulation of its structural evolution. We provide a fully open-source implementation of our method, as well as the training and testing examples with the stanene dataset.