Most real-world networks considered in the literature have a modular structure. Analysis of these real-world networks often are performed under the assumption that there is only one type of node. However, social and biochemical systems are often bipartite networks, meaning that there are two exclusive sets of nodes, and that edges run exclusively between nodes belonging to different sets. Here we address the issue of module detection in bipartite networks by comparing the performance of two classes of group identification methods - modularity maximization and clique percolation - on an ensemble of modular random bipartite networks. We find that the modularity maximization methods are able to reliably detect the modular bipartite structure, and that, under some conditions, the simulated annealing method outperforms the spectral decomposition method. We also find that the clique percolation methods are not capable of reliably detecting the modular bipartite structure of the bipartite model networks considered.