Simulator-based models are models for which the likelihood is intractable but simulation of synthetic data is possible. Such models are often used to describe complex real-world phenomena, and as such can often be misspecified in practice. Unfortunately, existing Bayesian approaches for simulators are known to perform poorly in misspecified settings. In this paper, we propose a novel approach based on the posterior bootstrap which gives a highly-parallelisable Bayesian inference algorithm for simulator-based models. Our approach is based on maximum mean discrepancy estimators, which also allows us to inherit their robustness properties.