The Networks, Norms, and HIV/STI Risk Among Youth (NNAHRAY) study consists of observational data on a network composed of interconnected sexual and injection drug use partnerships. Like many interpersonal networks, two persons who are not engaged in a partnership may still be associated via transitive connections. Thus, when estimating causal effects of an intervention, statistical methods should account for both (1) long-range outcome dependence between two persons on the network and (2) arbitrary forms of interference whereby one person's outcome is affected by other persons' exposures. In recent work, we developed the auto-g-computation algorithm for causal inference on a single realization of a network of connected units. This algorithm relied on certain coding estimators, which are generally inefficient by virtue of censoring observations and may be unstable even in moderately dense networks. In this work, we develop a Bayesian auto-g-computation algorithm which incorporates data on the entire network and is substantially more efficient than the coding estimator. We then evaluate the effect of prior incarceration on HIV, STI, and Hepatitis C prevalence on the NNAHRAY network.