We consider optimising bone neotissue growth in a 3D scaffold during dynamic perfusion bioreactor culture. The goal is to choose design variables by optimising two conflicting objectives: (i) maximising neotissue growth and (ii) minimising operating cost. Our contribution is a novel extension of Bayesian multi-objective optimisation to the case of one black-box (neotissue growth) and one analytical (operating cost) objective function, that helps determine, within a reasonable amount of time, what design variables best manage the trade-off between neotissue growth and operating cost. Our method is tested against and outperforms the most common approach in literature, genetic algorithms, and shows its important real-world applicability to problems that combine black-box models with easy-to-quantify objectives like cost.