We present an efficient Bayesian online learning algorithm for clustering vectors of binary values based on a well known model, the mixture of Bernoulli profiles. The model includes conjugate Beta priors over the success probabilities and maintains discrete probability distributions for cluster assignments. Clustering is then formulated as inference in a factor graph which is solved efficiently using online approximate message passing. The resulting algorithm has three key features: a) it requires only a single pass across the data and can hence be used on data streams, b) it maintains the uncertainty of parameters and cluster assignments, and c) it implements an automatic step size adaptation based on the current model uncertainty. The model is tested on an artificially generated toy dataset and applied to a large scale real-world data set from online advertising, the data being online ads characterized by the set of keywords to which they have been subscribed. The proposed approach scales well for large datasets, and compares favorably to other clustering algorithms on the ads dataset. As a concrete application to online advertising we show how the learned model can be used to recommend new keywords for given ads.