Taking advantage of both naturally derived polymers and nanostructured materials, in the current study, we propose new multicomponent hydrogels double reinforced with two complementary nano-fillers developed for bioprinting-based tissue engineering applications. In a bioinspired approach, cellulose nanofibrils (CNFs) and polyhedral silsesquioxanes (PSS) nanoparticles were embedded in a proteinaceous-polysaccharidic matrix. To synthesize a robust platform for 3D bioprinting, methacrylate-modified biopolymers were crosslinked using UV-light to provide optimal conditions for cell encapsulation purposes. The nanocomposite bioinks were supplemented with bone morphogenetic protein 2 (BMP2) as potent osteogenic factor to maximize the function of preosteoblasts already engaged to the osteogenic lineage. The 3D-scaffolds’ morphology was investigated focusing on PSS dispersion, porosity, and geometrical features of constructs. Swelling results showed that all the samples maintained their hydrophilic character with a slight decreasing tendency of the swelling capacity when PSS was incorporated. The in vitro cytocompatibility tests proved the beneficial influence of CNFs and PSS additives in the process of cell growth. In vivo studies revealed that hydrogels supplemented with nanostructured fillers and BMP2 promote improved osteogenesis both in osteogenic and nonosteogenic regions proving that scaffolds reinforced with growth factors have a big potential to respond to the challenges of the biomaterials and could be a promising option for the regeneration of hard tissues.