Graph positive-unlabeled learning is an important task that tries to learn binary classification models from only positive and unlabeled (PU) nodes. While state-of-the-art methods focus on training graph neural networks, they frequently rely on weak objective functions derived solely from a given class prior probability or inferred exclusively from the graph structure, leading their performance significantly lags behind that of fully labeled counterparts. In this paper, we fill this gap by treating unlabeled nodes as samples ambiguously labeled as both positive and negative, and by introducing a learning method called Bootstrap Label Disambiguation (BLD), which progressively resolves label ambiguities during the training of binary classifiers. BLD comprises a node representation learning module via bootstrapping and a novel central region-based label disambiguation strategy. The learning module leverages both previous representations and the derived positive centriod as targets to train positive-aligned representations, eliminating the need for a prior. Consequently, the disambiguation strategy constructs a central-region to identify ambiguous nodes and steadily transforms them into effective supervision. Extensive experiments on a range of real-world datasets show that our BLD method significantly outperforms existing approaches and in many cases even surpasses fully labeled classification models. The source code is available at https://github.com/yunyun85/BLD.