Bipartite graph learning aims to embed nodes into a low-dimensional representation, which has been successfully devoted to diverse network analysis tasks, such as recommender systems, drug discovery, etc. Recently, knowledge-aware contrastive learning models have achieved excellent performance in bipartite graph learning by utilising abundant factual information in knowledge graphs to alleviate the data sparsity issue. In this paper, we propose a Bipartite Graph Contrastive Learning architecture with Knowledge-aware Diffusion-Enhanced (BGCL-KDE) for bipartite graph learning. Specifically, we first construct an attention-aware matrix into graph neural networks to identify the importance between two types of nodes for generating attention-aware and knowledge-aware node feature aggregation, which is constructed to preserve the importance between two types of nodes by a random walk with a restart strategy. Then, a knowledge-aware contrastive view is generated by a proposed guided diffusion model, which utilises strongly task-relevant node knowledge to enhance node semantic information. Comprehensive experiments on bipartite graph datasets from two application domains containing recommender systems and drug discovery reveal the superiority of our BGCL-KDE on diverse state-of-the-art approaches. Notably, the ablation study demonstrates the significant effectiveness of the attention-aware matrix. Our datasets and source code are available1https://github.com/Ding-guang-hua/BGCL_KDE.