We propose a method for extracting hierarchical backbones from a bipartite network. Our method leverages the observation that a hierarchical relationship between two nodes in a bipartite network is often manifested as an asymmetry in the conditional probability of observing the connections to them from the other node set. Our method estimates both the importance and direction of the hierarchical relationship between a pair of nodes, thereby providing a flexible way to identify the essential part of the networks. Using semi-synthetic benchmarks, we show that our method outperforms existing methods at identifying planted hierarchy while offering more flexibility. Application of our method to empirical datasets---a bipartite network of skills and individuals as well as the network between gene products and Gene Ontology (GO) terms---demonstrates the possibility of automatically extracting or augmenting ontology from data.