Three-dimensional (3D) bioprinting offers precise spatial control for fabricating cell-laden constructs, yet bioink development remains constrained by labor-intensive trial-and-error experiments and fragmented reporting. Conventional machine-learning pipelines can support quantitative property prediction but generally require structured inputs and therefore do not natively use the formulation knowledge embedded in narrative literature. Large language models (LLMs), particularly when combined with domain-adapted information extraction, retrieval-augmented generation (RAG), and knowledge graphs, offer a complementary route for converting literature into traceable design evidence. This critical conceptual review examines how these technologies could support bioink knowledge extraction, formulation recommendation, and design-build-test-learn (DBTL) workflow coordination. Because direct experimental applications of LLMs to bioink design remain scarce, we explicitly distinguish demonstrated evidence in bioprinting from transferable evidence in biomedical natural-language processing, materials informatics, chemistry, and autonomous experimentation, and from prospective biofabrication concepts. We outline a provenance-aware Bioink Knowledge Graph (BioKG), clarify the complementary roles of LLMs, numerical generative models, Bayesian optimization, computer vision, and robotic control, and provide tissue-specific workflow scenarios and a minimum proof-of-concept evaluation framework. Key limitations include conflicting and heterogeneous evidence, cell-type-specific constraints, hallucination, limited benchmark datasets, and the absence of end-to-end validation. The resulting framework should therefore be interpreted as an evidence-bounded research roadmap rather than as a clinically or experimentally validated autonomous bioprinting system.