Data-driven site characterization (DDSC) aids geotechnical engineering by inferring and mapping soil parameters of the subsurface domain. In practice, the limited availability of site investigation data may hinder the performance of traditional machine learning methods and implies significant uncertainty in the predictions, which is typically not quantified. In this study, a framework for Bayesian site characterization (BaySiC) is applied on a benchmark example. Adopting Bayesian statistics enables the framework to deal with small training data sets and allows for coherent quantification of uncertainty, which is valuable to engineering practice for assessing the reliability and the determining characteristic values. BaySiC uses site investigation data to infer statistical estimators of cone penetration test (CPT) parameters and their dependence, as well as to learn spatial correlations. Consecutively, it generates a three-dimensional (3D) map of the subsurface by predicting the CPT parameter values and classifying the material type over the soil domain. For the benchmark example, the study formulated two models within the BaySiC framework and demonstrated their conduct in several cases of varying complexity. Eventually, the performance of the models was evaluated and compared in both deterministic and probabilistic terms. One of the models proved highly effective in predicting the material type at new locations of the subsurface domain, whereas the other provided accurate mapping of the CPT parameters even in complex stratigraphic cases. Also, investigating and comparing the results of the models led to insights regarding the effectiveness of their formulation. Moreover, the paper used hypothesis testing as a means of assessing the predictive power of the model independently from the validation data set. Stemming from the benchmark example, the paper draws conclusions that are meaningful to geotechnical engineering and decision-making.