We consider the task of simultaneous clustering of the two node sets involved in a bipartite network. The approach we adopt is based on use of the exact integrated complete likelihood for the latent blockmodel. Using this allows one to infer the number of clusters as well as cluster memberships using a greedy search. This gives a model-based clustering of the node sets. Experiments on simulated bipartite network data show that the greedy search approach is vastly more scalable than competing Markov chain Monte Carlo-based methods. Application to a number of real observed bipartite networks demonstrate the algorithms discussed.