Reservoir computing is a growing paradigm for simplified training of recurrent neural networks, with a high potential for hardware implementations. Numerous experiments in optics and electronics yield comparable performance with digital state-of-the-art algorithms. Many of the most recent works in the field focus on large-scale photonic systems, with tens of thousands of physical nodes and arbitrary interconnections. While this trend significantly expands the potential applications of photonic reservoir computing, it also complicates the optimisation of the high number of hyper-parameters of the system. In this work, we propose the use of Bayesian optimisation for efficient exploration of the hyper-parameter space in a minimum number of iteration. We test this approach on a previously reported large-scale experimental system, compare it with the commonly used grid search, and report notable improvements in performance and the number of experimental iterations required to optimise the hyper-parameters. Bayesian optimisation thus has the potential to become the standard method for tuning the hyper-parameters in photonic reservoir computing.