A functional bioink with potential in bone tissue engineering must be subjected to critical investigation throughout its intended lifespan. The aim of this study was to develop alginate-gelatin-based (Alg-Gel) multicomponent bioinks systematically and to assess the short- and long-term exposure responses of human bone marrow stromal cells (hBMSCs) printed within these bioinks with and without crosslinking. The first generation of bioinks was established by incorporating a range of cellulose nanofibrils (CNFs), to evaluate their effect on viscosity, printability and cell viability. Adding CNFs to Alg-Gel solution increased viscosity and printability without compromising cell viability. In the second generation of bioinks, the influence of nano-hydroxyapatite (nHA) on the performance of the optimized Alg-Gel-CNF formulation was investigated. The addition of nHA increased the viscosity and improved printability, and an adjustment in alginate concentration improved the stability of the structures in long-term culture. The third generation bioink incorporated RGD-functionalized alginate to support cell attachment and osteogenic differentiation. The optimized bioink composition exhibited improved printability, structural integrity in long-term culture and high hBMSC viability. In addition, the final bioink composition, RGD-Alg-Gel-CNF-nHA, showed osteogenic potential: production of the osteogenic marker proteins (Runx2, OCN), enzyme (ALP), and gene expression (Runx2, Ocn). A further aim of the study was to evaluate the osteogenic functionality of cells released from the structures after bioprinting. Cells were printed in two bioinks with different viscosities and incubated at 37 °C in growth medium without additional CaCl2. This caused gelatin to dissolve, releasing the cells to attach to tissue culture plates. The results demonstrated differences in hBMSC osteogenic differentiation. Moreover, the osteogenic differentiation of the released cells was different from that of the embedded cells cultured in 3D. Thus, this systematic investigation into bioink development shows improved results through the generations and sheds light on the biological effects of the bioprinting process., (Creative Commons Attribution license.)