Small-angle X-ray scattering (SAXS) has become an increasingly popular technique for characterizing the solution ensemble of flexible biomolecules. However, data resulting from SAXS is typically low-dimensional and is therefore difficult to interpret without additional structural knowledge. In theory, molecular dynamics (MD) trajectories can provide this information, but conventional simulations rarely sample the complete ensemble. Here, we demonstrate that accelerated MD simulations can be used to produce higher quality models in shorter time scales than standard simulations, and we present an iterative Bayesian Monte Carlo method that is able to identify multistate ensembles without overfitting. This methodology is applied to several ubiquitin trimers to demonstrate the effect of linkage type on the solution states of the signaling protein. We observe that the linkage site directly affects the solution flexibility of the trimer and theorize that this difference in plasticity contributes to their disparate roles in vivo.