Bioactive glasses have been used for bone regeneration applications thanks to their excellent osteoconductivity, an osteostimulatory effect, and high degradation rate, releasing biologically active ions. Besides these properties, mesoporous bioactive glasses (MBG) are specific for their highly ordered mesoporous channel structure and high specific surface area, making them suitable for drug and growth factor delivery. In the present study, calcium (Ca) (15 mol%) in MBG was partially and fully substituted with zinc (Zn), known for its osteogenic and antimicrobial properties. Different MBG were synthesized, containing 0, 5, 10, or 15 mol% of Zn. Up to 7 wt.% of Zn-containing MBG could be mixed into an alginate-methylcellulose blend (algMC) while maintaining rheological properties suitable for 3D printing of scaffolds with sufficient shape fidelity. The suitability of these composites for bioprinting applications has been demonstrated with immortalized human mesenchymal stem cells. Uptake of Ca and phosphorus (P) (phosphate) ions by composite scaffolds was observed, while the released concentration of Zn2+ corresponded to the initial amount of this ion in prepared glasses, suggesting that it can be controlled at the MBG synthesis step. The study introduces a tailorable bioprintable material system suitable for bone tissue engineering applications.