Extrusion-based bioprinting requires hydrogel materials with suitable rheological behavior, structural stability, and bio-related properties; however, the relationships among composition, network structure, and printing performance in multicomponent hydrogel systems remain insufficiently understood. In this study, a GG/SS/PVA/GEL composite hydrogel was developed and optimized using single-factor experiments combined with Box–Behnken response surface methodology. Rheological analysis, Fourier transform infrared spectroscopy, and scanning electron microscopy were further used to characterize the optimized system. The optimal formulation was identified as 0.14 g of GG, 0.60 g of SS, and 2.3 g of PVA. This formulation achieved a comprehensive score of 87 with a prediction error of less than 5%. The optimized hydrogel exhibited pronounced shear-thinning behavior, a printing fidelity of 98.6–101.4%, a maximum swelling ratio of approximately 403.5%, and an enzymatic degradation rate of 68.5%, together with a relatively uniform interconnected porous structure. These results indicate that the optimized composite hydrogel is a promising printable material candidate and provide a useful basis for formulation design in extrusion-based hydrogel systems.