Anchor-based bipartite graph methods provide linear scalability for multi-view clustering, but most of them construct graphs in the original feature space, where high dimensionality distorts the proximity between samples and anchors and degrades graph quality. In addition, the K-means step commonly used to discretize spectral embeddings produces different cluster assignments across random seeds. To address these limitations, this paper proposes Projection-Enhanced Bipartite Graph Learning (PEBGL), a unified framework that jointly performs subspace projection, bipartite graph construction, consensus graph fusion with adaptive view weighting, and discrete label assignment. Every subproblem admits a closed-form or deterministic solution, so the algorithm runs in linear time and produces reproducible cluster labels for any fixed initialization. Experiments on six benchmark datasets demonstrate that PEBGL achieves consistently competitive accuracy across all evaluation settings and improves over the strongest baseline by up to 4.8 percentage points. These results confirm the effectiveness and generality of the proposed framework.