Random utility theory models an agent's preferences on alternatives by drawing a real-valued score on each alternative (typically independently) from a parameterized distribution, and then ranking according to scores. A special case that has received significant attention is the Plackett-Luce model, for which fast inference methods for maximum likelihood estimators are available. This paper develops conditions on general, random utility models that enable fast inference within a Bayesian framework through MC-EM, providing unimodal log-likelihood functions. Results on both real-world and simulated data provide support for the scalability of the approach, despite its flexibility.