In traditional clustering, every data point is assigned to at least one cluster. On the other extreme, One Class Clustering algorithms proposed recently identify a single dense cluster and consider the rest of the data as irrelevant. However, in many problems, the relevant data forms multiple natural clusters. In this paper, we introduce the notion of Bregman bubbles and propose Bregman Bubble Clustering (BBC) that seeks k dense Bregman bubbles in the data. We also present a corresponding generative model, Soft BBC, and show several connections with Bregman Clustering, and with a One Class Clustering algorithm. Empirical results on various datasets show the effectiveness of our method.