Contrast Enhanced Ultrasound (CEUS) is a sensitive imaging technique to assess tissue vascularity and it can be particularly useful in early detection and grading of arthritis. In a recent study we have shown that a Gamma-variate can accurately quantify synovial perfusion and it is flexible enough to describe many heterogeneous patterns. However, in some cases the heterogeneity of the kinetics can be such that even the Gamma model does not properly describe the curve, with a high number of outliers. In this work we apply to CEUS data the single compartment recirculation model (SCR) which takes explicitly into account the trapping of the microbubbles contrast agent by adding to the single Gamma-variate model its integral. The SCR model, originally proposed for dynamic-susceptibility magnetic resonance imaging, is solved here at pixel level within a Bayesian framework using Variational Bayes (VB). We also include the automatic relevant determination (ARD) algorithm to automatically infer the model complexity (SCR vs. Gamma model) from the data. We demonstrate that the inclusion of trapping best describes the CEUS patterns in 50% of the pixels, with the other 50% best fitted by a single Gamma. Such results highlight the necessity of the use ARD, to automatically exclude the irreversible component where not supported by the data. VB with ARD returns precise estimates in the majority of the kinetics (88% of total percentage of pixels) in a limited computational time (on average, 3.6 min per subject). Moreover, the impact of the additional trapping component has been evaluated for the differentiation of rheumatoid and non-rheumatoid patients, by means of a support vector machine classifier with backward feature selection. The results show that the trapping parameter is always present in the selected feature set, and improves the classification.