We review, propose, and compare several Bayesian data synthesizers with different differential privacy guarantees that can be used by data stewards for microdata dissemination with privacy protection. The pseudo posterior mechanism achieves an asymptotic differential privacy guarantee and a variant of it can provide faster convergence. The newly proposed censoring mechanism embedded in the pseudo posterior mechanism censors the pseudo likelihood of every record within [exp(-epsilon/2), exp(epsilon/2)], which provides a stronger, non-asymptotic differential privacy guarantee. Through a series of simulation studies with bounded, univariate data and an application to sample of the Survey of Doctoral Recipients where a beta regression synthesizer is utilized, we demonstrate that the pseudo posterior mechanism creates synthetic data with the highest utility at the price of a weaker, asymptotic privacy guarantee, while the censoring mechanism embedded in the pseudo posterior mechanism produces synthetic data with a stronger, non-asymptotic privacy guarantee at the cost of slightly reduced utility. The perturbed histogram is included for comparison.