This paper presents a novel methodology to auto-tune an Unscented Kalman Filter (UKF). It involves using a Two-Stage Bayesian Optimisation (TSBO), based on a t-Student Process to optimise the process noise parameters of a UKF for vehicle sideslip angle estimation. Our method minimises performance metrics, given by the average sum of the states' and measurement' estimation error for various vehicle manoeuvres covering a wide range of vehicle behaviour. The predefined cost function is minimised through a TSBO which aims to find a location in the feasible region that maximises the probability of improving the current best solution. Results on an experimental dataset show the capability to tune the UKF in 79.9% less time than using a genetic algorithm (GA) and the overall capacity to improve the estimation performance in an experimental test dataset of 9.9% to the current state-of-the-art GA.