It is shown that the Bayesian bootstrap approximation to the posterior distribution of the unknown mean (with respect to a Dirichlet process prior) is more accurate than both the standard normal approximation and the bootstrap approximation. It is also shown that the Bayesian bootstrap approximation to the sampling distribution of the sample average is not as accurate as the bootstrap approximation.
"On a Second-Order Asymptotic Property of the Bayesian Bootstrap Mean." Ann. Statist. 17 (2) 705 - 710, June, 1989. https://doi.org/10.1214/aos/1176347136