In theoretical ecology, simple stochastic models that satisfy two basic conditions about the distribution of niche values and feeding ranges have proved successful in reproducing the overall structural properties of real food webs, using species richness and connectance as the only input parameters. Recently, more detailed models have incorporated higher levels of constraint in order to reproduce the actual links observed in real food webs. Here, building on previous stochastic models of consumer-resource interactions between species, we propose a highly parsimonious model that can reproduce the overall bipartite structure of cooperative partner-partner interactions, as exemplified by plant-animal mutualistic networks. Our stochastic model of bipartite cooperation uses simple specialization and interaction rules, and only requires three empirical input parameters. We test the bipartite cooperation model on ten large pollination data sets that have been compiled in the literature, and find that it successfully replicates the degree distribution, nestedness and modularity of the empirical networks. These properties are regarded as key to understanding cooperation in mutualistic networks. We also apply our model to an extensive data set of two classes of company engaged in joint production in the garment industry. Using the same metrics, we find that the network of manufacturer-contractor interactions exhibits similar structural patterns to plant-animal pollination networks. This surprising correspondence between ecological and organizational networks suggests that the simple rules of cooperation that generate bipartite networks may be generic, and could prove relevant in many different domains, ranging from biological systems to human society.