Conventional solvent-based polyurethane (PU) adhesives, widely utilized in the flexible packaging industry, have raised environmental concerns due to their emission of volatile organic compounds during use. Therefore, there is growing interest in the development of solvent-free PU adhesives that offer improved cooking resistance and use environmentally friendly raw materials. Herein, eco-friendly solvent-free PU adhesives derived from biomass sources for flexible packaging applications are reported. Specifically, two biobased polyols were prepared through the ring-opening reaction of epoxy soybean oil with rosin and the reaction of castor oil with 2,2-dimethylolpropionate. The biobased polyols, together with polyester polyols, were then mixed with another adhesive component (prepolymers containing isocyanate) and cured at room temperature, resulting in the PU bioadhesives. The impact of the polyols on the cooking resistance of the bioadhesives was evaluated by peel strength and package-cooking tests. The results revealed that the addition of 10 wt % epoxidized soybean oil/rosin achieved the best adhesive performance. The peel force before and after boiling treatment reached 7.48 and 5.30 N, respectively, an increase of 18.7 and 21.3%, respectively, compared with that of the samples without additives. The introduction of a long-chain fatty acid from vegetable oil and the rigid tricyclic phenanthrene skeleton structure of rosin into the PU adhesives effectively enhanced their hydrothermal and cooking resistance properties. The biomass-based solvent-free PU adhesives developed in this study hold promising potential for partially substituting solvent-based PU adhesives for flexible packaging applications.