This paper addresses learning of the tire-friction curve for road vehicles, using a batch of wheel-speed and inertial measurements. We formulate a Bayesian approach based on recent advances in particle filtering and Markov chain Monte-Carlo methods. The unknown function mapping the wheel slip to tire friction is modeled as a Gaussian process (GP) that is included in a dynamic vehicle model relating the GP to the vehicle state. The approach is nonparametric and learns the probability density function of the tire friction, from which explicit estimates can be extracted. One benefit of the method is that it is not subject to overfitting issues. We illustrate the efficacy of the method for a set of simulated step-steer maneuvers. The results show that the method can accurately identify the nonlinear tire-friction curves, even for a limited amount of data.