The rapid growth of social media has caused tremendous effects on information propagation, raising extreme challenges in detecting rumors. Existing rumor detection methods typically exploit the reposting propagation of a rumor candidate for detection by regarding all reposts to a rumor candidate as a temporal sequence and learning semantics representations of the repost sequence. However, extracting informative support from the topological structure of propagation and the influence of reposting authors for debunking rumors is crucial, which generally has not been well addressed by existing methods. In this article, we organize a claim post in circulation as an ad hoc event tree, extract event elements, and convert it into bipartite ad hoc event trees in terms of both posts and authors, i.e., author tree and post tree. Accordingly, we propose a novel rumor detection model with hierarchical representation on the bipartite ad hoc event trees called BAET. Specifically, we introduce word embedding and feature encoder for the author and post tree, respectively, and design a root-aware attention module to perform node representation. Then we adopt the tree-like RNN model to capture the structural correlations and propose a tree-aware attention module to learn tree representation for the author tree and post tree, respectively. Extensive experimental results on two public Twitter datasets demonstrate the effectiveness of BAET in exploring and exploiting the rumor propagation structure and the superior detection performance of BAET over state-of-the-art baseline methods.