The goal of data-driven nonlinear control problems is to guarantee stability or safety of an unknown system. We consider a method based on Control Certificate Functions (CCFs) that uses Gaussian Process (GP) regression to learn unknown quantities for control affine dynamics. Computing the GP estimator can become prohibitively expensive for large datasets, which is an issue since speed is critical in real time control systems. We introduce a random feature approximation of the affine compound kernel to speed up training and prediction time. To ensure that the controller can be robust to these approximations, we provide an error analysis on the approximate mean and variance estimates.Finally, we propose a fast and robust convex optimization based min-norm controller using the error bounds and present preliminary experiments comparing the random features approximation to kernel methods.