Significant differences in protein structures hinder the generalization of existing drug-target interaction (DTI) models, which often rely heavily on pre-learned binding principles or detailed annotations. In contrast, BioBridge designs an Inductive-Associative pipeline inspired by the workflow of scientists who base their accumulated expertise on drawing insights into novel drug-target pairs from weakly related references. BioBridge predicts novel drug-target interactions using limited sequence data, incorporating multi-level encoders with adversarial training to accumulate transferable binding principles. On these principles basis, BioBridge employs a dynamic prototype meta-learning framework to associate insights from weakly related annotations, enabling robust predictions for previously unseen drug-target pairs. Extensive experiments demonstrate that BioBridge surpasses existing models, especially for unseen proteins. Notably, when only homologous protein binding data is available, BioBridge proves effective for virtual screening of the epidermal growth factor receptor and adenosine receptor, underscoring its potential in drug discovery.