Sample efficient learning of manipulation skills poses a major challenge in robotics. While recent approaches demonstrate impressive advances in the type of task that can be addressed and the sensing modalities that can be incorporated, they still require large amounts of training data. Especially with regard to learning actions on robots in the real world, this poses a major problem due to the high costs associated with both demonstrations and real-world robot interactions. To address this challenge, we introduce BOpt-GMM, a hybrid approach that combines imitation learning with own experience collection. We first learn a skill model as a dynamical system encoded in a Gaussian Mixture Model from a few demonstrations. We then improve this model with Bayesian optimization building on a small number of autonomous skill executions in a sparse reward setting. We demonstrate the sample efficiency of our approach on multiple complex manipulation skills in both simulations and real-world experiments. Furthermore, we make the code and pre-trained models publicly available at http://bopt-gmm.cs.uni-freiburg.de.