Matching suitable jobs provided by employers with qualified candidates is a crucial task for online recruitment. Typically, candidates and employers have specific expectations in recruitment market, leading them to prefer similar jobs and candidates, respectively. Metric learning provides a promising way to capture the similarity propagation between candidates and jobs. However, existing metric learning technologies rely on symmetric distance measures, which fail to model the asymmetric relationships of bilateral users (i.e., candidates and employers) in the two-way selective process of recruitment scenarios. In addition, the behavior of users (e.g., candidates) is highly affected by the actions and feedback of their counterparts (e.g., employers). These effects can hardly be captured by the existing person-job fit methods which primarily explore homogeneous and undirected graphs. To address these problems, we propose a quasi-metric learning framework to capture the similarity propagation between candidates and jobs while modeling their asymmetric relations for bilateral person-job fit. Specifically, we propose a quasi-metric space that not only satisfies the triangle inequality rule to capture the fine-grained similarity between candidates and jobs, but also incorporates a tailored asymmetric measure to model the two-way selection process of bilateral users in online recruitment. More importantly, the proposed quasi-metric learning framework can theoretically model recruitment rules from similarity and competitiveness perspectives, making it seamlessly align with bilateral person-job fit scenarios. To explore the mutual effects of two-sided users on each other, we first organize candidates, employers, and their different-typed interactions into a heterogeneous relation graph, and then propose a relation-aware graph convolution network to capture the mutual effects of users with their bilateral behaviors. Extensive experiments on several real-world datasets demonstrate the effectiveness of the proposed quasi-metric learning framework and bilateral person-job fit model.