||Wrapper feature selection can lead to highly accurate classifications. However, the computational costs for this are very high in general. Bayesian Optimization on the other hand has already proven to be very efficient in optimizing black box functions. This approach uses Bayesian Optimization in order to minimize the number of evaluations, i.e. the training of models with different feature subsets. We propose four different ways to set up the objective function for the Bayesian optimization. On 14 different classification datasets the approach is compared against 14 other established feature selection methods, including other wrapper methods, but also filter methods and embedded methods. We use gaussian processes and random forests for the surrogate model. The classifiers which are applied to the selected feature subsets are logistic regression and naive bayes. We compare all the different feature selection methods against each other by comparing their classification accuracies and runtime. Our approach shows to keep up with the most established feature selection methods, but the evaluation also shows that the experimental setup does not value the feature selection enough. Concluding, we give guidelines how an experimental setup can be more appropriate and several concepts are provided of how to develop the Bayesian optimization for wrapper feature selection further.