Searching on bipartite graphs serves as a fundamental task for various real-world applications, such as recommendation systems, database retrieval, and document querying. Conventional approaches rely on similarity matching in continuous Euclidean space of vectorized node embeddings. To handle intensive similarity computation efficiently, hashing techniques for graph-structured data have emerged as a prominent research direction. However, despite the retrieval efficiency in Hamming space, previous studies have encountered catastrophic performance decay. To address this challenge, we investigate the problem of hashing with Graph Convolutional Network for effective Top-N search. Our findings indicate the learning effectiveness of incorporating hashing techniques within the exploration of bipartite graph reception fields, as opposed to simply treating hashing as post-processing to output embeddings. To further enhance the model performance, we advance upon these findings and propose Bipartite Graph Contrastive Hashing (BGCH+). BGCH+ introduces a novel dual augmentation approach to both intermediate information and hash code outputs in the latent feature spaces, thereby producing more expressive and robust hash codes within a dual self-supervised learning paradigm. Comprehensive empirical analyses on six real-world benchmarks validate the effectiveness of our dual feature contrastive learning in boosting the performance of BGCH+ compared to existing approaches.