Cluster ensembles provide a framework for combining multiple base clusterings of a dataset to generate a stable and robust consensus clustering. There are important variants of the basic cluster ensemble problem, notably including cluster ensembles with missing values, as well as row-distributed or column-distributed cluster ensembles. Existing cluster ensemble algorithms are applicable only to a small subset of these variants. In this paper, we propose Bayesian Cluster Ensembles (BCE), which is a mixed-membership model for learning cluster ensembles, and is applicable to all the primary variants of the problem. We propose two methods, respectively based on variational approximation and Gibbs sampling, for learning a Bayesian cluster ensemble. We compare BCE extensively with several other cluster ensemble algorithms, and demonstrate that BCE is not only versatile in terms of its applicability, but also outperforms the other algorithms in terms of stability and accuracy.