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Public transportation operates in an environment which, due to its nature of numerous possibly influencing factors, is highly stochastic. This makes predictions of arrival times difficult, yet it’s important to be accurate in order to adhere to travelers expectations. In this study, the focus is on quantifying uncertainty around travel-time predictions as a means to improve the reliability of predictions in the context of public transportation. This is done by comparing Prediction Interval Coverage Probability (PICP) and Normalized Mean Prediction Interval Length (NMPIL). Three models, with two transformations of the response variable, were evaluated on real travel data from Skånetrafiken. The focus of the study was on examining a specific urban bus route, namely line 5 in Malmö, Sweden. The results indicated that a transformation based on the firstDifference achieved a better performance overall, but the results on a stopwise basis varied along the route. In terms of models, the uncertainty quantification revealed that Quantile Regression could be more appropriate at capturing data intervals which provide better coverage but at a shorter interval length, thus being more precise in its predictions. This is likely relatable to the robustness of the model and it being able to deal with extreme observations. A comparison with the current prediction model, which is agnostic in this study, revealed that the proposed point estimates from the Gaussian Process model based on the  firstDifference transformation outperformed the agnostic model on several stops. As such, further research is proposed as there is means for improvement in the current implementation.