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The SEparator for CApture Reactions (SECAR) is a next-generation recoil separator system at the Facility for Rare Isotope Beams (FRIB) designed for the direct measurement of capture reactions on unstable nuclei in inverse kinematics. To maximize the performance of this system, stringent requirements on the beam alignment to the central beam axis and on the ion-optical settings need to be achieved. These can be difficult to attain through manual tuning by human operators without potentially leaving the system in a sub-optimal and irreproducible state. In this work, we present the first development of online Bayesian optimization with a Gaussian process model to tune an ion beam through a nuclear astrophysics recoil separator. We show that this method achieves small incoming angular deviations (\textless 1 mrad) in an efficient and reproducible manner that is at least three times faster than standard hand-tuning. Additionally, we present a Bayesian method for experimental optimization of the ion optics, and show that it validates the nominal theoretical ion-optical settings of the device, and improves the mass separation by 32\% for some beams.