Tissue-engineered bone tissue grafts are a promising alternative to the more conventional use of natural donor bone grafts. However, choosing an appropriate biomaterial/scaffold to sustain cell survival, proliferation, and differentiation in a 3D environment remains one of the most critical issues in this domain. Recently, chitosan/gelatin/genipin (CGG) hybrid scaffolds have been proven as a more suitable environment to induce osteogenic commitment in undifferentiated cells when doped with graphene oxide (GO). Some concern is, however, raised towards the use of graphene and graphene-related material in medical applications. The purpose of this work was thus to check if the osteogenic potential of CGG scaffolds without added GO could be increased by improving the medium diffusion in a 3D culture of differentiating cells. To this aim, the level of extracellular matrix (ECM) mineralization was evaluated in human bone-marrow-derived stem cell (hBMSC)-seeded 3D CGG scaffolds upon culture under a perfusion flow in a dedicated custom-made bioreactor system. One week after initiating dynamic culture, histological/histochemical evaluations of CGG scaffolds were carried out to analyze the early osteogenic commitment of the culture. The analyses show the enhanced ECM mineralization of the 3D perfused culture compared to the static counterpart. The results of this investigation reveal a new perspective on more efficient clinical applications of CGG scaffolds without added GO.