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We have evaluated the data-efficient Bayesian optimization method for the specific task of injection tuning in a circular accelerator. In this paper, we describe the implementation of this method at the Karlsruhe Research Accelerator with up to nine tuning parameters, including the determination of the associated hyperparameters. We show that the Bayesian optimization method outperforms manual tuning and the commonly used Nelder-Mead optimization algorithm both in simulation and experiment. The algorithm was also successfully used to ease the commissioning phase after the installation of new injection magnets and is regularly used during accelerator operations. We demonstrate that the introduction of context variables that include intra-bunch scattering effects, such as the Touschek effect, further improves the control and robustness of the injection process.