This work proposes a framework for simulation-based and surrogate-based reduced space Bayesian optimization of process flowsheets. The framework uses global sensitivity analysis for dimensionality reduction via the identification of critical process variables that contribute significantly to the variability of the objective function (e.g. productivity and operating costs). Both simulation- and surrogate-based algorithms are applied to a biopharmaceutical and a chemical process simulator for the production of plasmid DNA and dimethyl ether (DME), respectively. Their capabilities are assessed in terms of the trade-off between computational effectiveness and solution accuracy. Results indicate that simulation-based Bayesian optimization achieves better objective function values, while surrogate-based Bayesian optimization is more computationally effective.