This work presents a methodology to estimate tire parameters and their uncertainty using a Bayesian optimization approach. The literature mainly considers the estimation of tire parameters but lacks an evaluation of the parameter identification quality and the required slip ratios for an adequate model fit. Therefore, we examine the use of Stochastical Variational Inference as a methodology to estimate both - the parameters and their uncertainties. We evaluate the method compared to a state-of-the-art Nelder-Mead algorithm for theoretical and real-world application. The theoretical study considers parameter fitting at different slip ratios to evaluate the required excitation for an adequate fitting of each parameter. The results are compared to a sensitivity analysis for a Pacejka Magic Formula tire model. We show the application of the algorithm on real-world data acquired during the Abu Dhabi Autonomous Racing League and highlight the uncertainties in identifying the curvature and shape parameters due to insufficient excitation. The gathered insights can help assess the acquired data's limitations and instead utilize standardized parameters until higher slip ratios are captured. We show that our proposed method can be used to assess the mean values and the uncertainties of tire model parameters in real-world conditions and derive actions for the tire modeling based on our simulative study.