The recent revival of Bayesian optimization has caused widespread utilization of easily accessible and versatile tools in different areas, which involve the search for optimal design or decisions. This method, however, has not yet been explored within the field of renewable energy systems. This study aims to introduce the main benefits of the procedure to the community through the practical task of optimizing the design and operation of the Archimedes screw turbine (AST) in terms of maximizing the total rate of return for a specific installation. The optimal design is presented as a combination of inputs to a software simulation of a true AST. The contribution of this manuscript is threefold: (i) we present the complete procedure needed for optimal sizing of an energy system using Bayesian optimization, (ii) compare various implementations and configurations of the optimization method available under several recent open-source software frameworks and (iii) compare the single-objective with the multi-objective approach to optimization within the same scenario. Our experiments demonstrate superior results using Bayesian optimization in comparison to the standard baseline, both in terms of the time and number of model evaluations required to reach a good solution.