3D extrusion printing has been widely investigated for low-volume production of complex-shaped scaffolds for tissue regeneration. Gelatin methacryloyl (GelMA) is used as a baseline material for the synthesis of biomaterial inks, often with organic/inorganic fillers, to obtain a balance between good printability and biophysical properties. The present study demonstrates how 45S5 bioactive glass (BG) addition and GelMA concentrations can be tailored to develop GelMA composite scaffolds with good printability and buildability. The experimental results suggest that 45S5 BG addition consistently decreases the compression stiffness, irrespective of GelMA concentration, albeit within 20% of the baseline scaffold (without 45S5 BG). The optimal addition of 2 wt % 45S5 BG in 7.5 wt % GelMA was demonstrated to provide the best combination of printability and buildability in the 3D extrusion printing route. The degradation decreases and the swelling kinetics increases with 45S5 BG addition, irrespective of GelMA concentration. Importantly, the dissolution in simulated body fluid over 3 weeks clearly promoted the nucleation and growth of crystalline calcium phosphate particles, indicating the potential of GelMA-45S5 BG to promote biomineralization. The cytocompatibility assessment using human osteoblasts could demonstrate uncompromised cell proliferation or osteogenic marker expression over 21 days in culture for 3D printable 7.5 wt % GelMA −2 wt % 45S5 BG scaffolds when compared to 7.5 wt % GelMA. The results thus encourage further investigations of the GelMA/45S5 BG composite system for bone tissue engineering applications.