A novel organic–inorganic hybrid, based on SiO2-CaO-ZnO bioactive glass (BG) and polycaprolactone (PCL), associating the highly bioactive and versatile bioactive glass with clinically established PCL was examined. The BG–PCL hybrid is obtained by acid-catalyzed silica sol–gel process inside PCL solution either by direct or indirect printing. Apatite-formation tests in simulated body fluid (SBF) confirm the ion release along with the hybrid’s bone-like apatite forming. Kinetics differ significantly between directly and indirectly printed scaffolds, the former requiring longer periods to degrade, while the latter demonstrates faster calcium phosphate (CaP) formation. Remarkably, Zn diffusion and accumulation are observed at the surface within the newly formed active CaP layer. Zn release is found to be dependent on printing method and immersion medium. Investigation of BG at the atomic scale reveals the ambivalent role of Zn, capable of acting both as a network modifier and as a network former linking the BG silicate network. In addition, hMSCs viability assay proves no cytotoxicity of the Zn hybrid. LIVE/DEAD staining demonstrated excellent cell viability and proliferation for over seven weeks. Overall, this hybrid material either non-doped or doped with a metal trace element is a promising candidate to be translated to clinical applications for bone regeneration.