Existing algorithms for joint clustering and feature selection can be categorized as either global or local approaches. Global methods select a single cluster-independent subset of features, whereas local methods select cluster-specific subsets of features. In this paper, we present a unified probabilistic model that can perform both global and local feature selection for clustering. Our approach is based on a hierarchical beta-Bernoulli prior combined with a Dirichlet process mixture model. We obtain global or local feature selection by adjusting the variance of the beta prior. We provide a variational inference algorithm for our model. In addition to simultaneously learning the clusters and features, this Bayesian formulation allows us to learn both the number of clusters and the number of features to retain. Experiments on synthetic and real data show that our unified model can find global and local features and cluster data as well as competing methods of each type.