A challenge in the extrusion-based bioprinting is to find a bioink with optimal biological and physicochemical properties. The aim of this study was to evaluate the influence of wood-based cellulose nanofibrils (CNF) and bioactive glass (BaG) on the rheological properties of gelatin-alginate bioinks and the initial responses of bone cells embedded in these inks. CNF modulated the flow behavior of the hydrogels, thus improving their printability. Chemical characterization by SEM-EDX and ion release analysis confirmed the reactivity of the BaG in the hydrogels. The cytocompatibility of the hydrogels was shown to be good, as evidenced by the viability of human osteoblast-like cells (Saos-2) in cast hydrogels. For bioprinting, 4-layer structures were printed from cell-containing gels and crosslinked with CaCl2. Viability, proliferation and alkaline phosphatase activity (ALP) were monitored over 14 d. In the BaG-free gels, Saos-2 cells remained viable, but in the presence of BaG the viability and proliferation decreased in correlation with the increased viscosity. Still, there was a constant increase in the ALP activity in all the hydrogels. Further bioprinting experiments were conducted using human bone marrow-derived mesenchymal stem cells (hBMSCs), a clinically relevant cell type. Interestingly, hBMSCs tolerated the printing process better than Saos-2 cells and the ALP indicated BaG-stimulated early osteogenic commitment. The addition of CNF and BaG to gelatin-alginate bioinks holds great potential for bone tissue engineering applications.