Likelihood-based inference under the multispecies coalescent provides accurate estimates of species trees. However, maximum likelihood and Bayesian inference are both computationally very demanding. Pseudo-likelihood has been previously proposed as a computationally efficient alternative to full phylogenetic likelihood calculations in the context of maximum likelihood estimation. However, theoretical and practical aspects of pseudo-likelihood in the context of Bayesian inference have not been explored. In this work, we provide strong theoretical guarantees and an empirical evaluation of pseudo-likelihood-based Bayesian inference of species trees under the multispecies coalescent. Our contributions are threefold. First, we prove a bound on the convergence rate for species tree topology inference and a Bernstein-von Mises result for branch lengths under model misspecification. Second, we provide an empirical comparison of full- and pseudo-likelihood-based Bayesian inference on synthetic data. Finally, we demonstrate the practical scalability of pseudo-likelihood-based inference by analyzing two biological datasets.