In this article, we present Bayesian analysis of capture-recapture models for a closed population which allows for heterogeneity of capture probabilities between animals and bait/trap effects. We use a flexible discrete mixture model to account for the heterogeneity and behavioural effects. In addition we present a solid model selection criterion. Through illustrations with a motivating dataset, we demonstrate how Bayesian analysis can be applied in this setting and discuss some major benefits which result, including consideration of informative priors based on historical data.