The Mallows' model is a common location-scale family of ranking distributions. In the frequentist setting, estimation is challenging as the parameter space is high-dimensional and discrete, leading to slow, if not intractable, estimation. We propose a Bayesian procedure that allows for fast estimation of the Mallows' model via a posterior that can be expressed as a finite mixture of continuous parameter models. We demonstrate how prior distributions may be chosen to align Bayesian posteriors with those from the frequentist setting, allowing for substantial increases in estimation speed. In addition, we show how our procedure may be applied to various extensions of the Mallows' model in the literature. The model is applied to real grant panel review data to demonstrate fast preference aggregation and how to estimate its uncertainty.