Two-sample summary data Mendelian randomization is a popular method for assessing causality in epidemiology, by using genetic variants as instrumental variables. If genes exert pleiotropic effects on the outcome not entirely through the exposure of interest, this can lead to heterogeneous and (potentially) biased estimates of causal effect. We investigate the use of Bayesian model averaging to preferentially search the space of models with the highest posterior likelihood. We develop a Metropolis-Hasting algorithm to perform the search using the recently developed MR-RAPS as the basis for defining a posterior distribution that efficiently accounts for pleiotropic and weak instrument bias. We demonstrate how our general modeling approach can be extended from a standard one-component causal model to a two-component model, which allows a large proportion of SNPs to violate the InSIDE assumption. We use Monte Carlo simulations to illustrate our methods and compare it to several related approaches. We finish by applying our approach to investigate the causal role of cholesterol on the development age-related macular degeneration.