Three-dimensional (3D) bio-printing technology involves printing biological materials in a 3D space using the additive manufacturing method and computer-aided design. In this study, we used natural polymeric hydrogels as bio-inks as they can mimic the extracellular matrix environment, supporting cell proliferation and differentiation. This study aims to determine the appropriate printing conditions for various hydrogel systems to fabricate 1 cm3 cube structure. To produce bio-inks, we have utilized the Schiff base reaction mechanism by covalently bonding the amine groups in N,O-carboxymethyl chitosan (NOCC) with the aldehyde groups in other oxidized polysaccharides such as oxidized xanthan gum (OXG), aldehyde hyaluronic acid (AHA), and oxidized alginate (OA). The bio-inks, namely NOCC-OXG, NOCC-AHA, NOCC-AHA-Alg, and NOCC-AHA-OA, were evaluated for their printability. The 3DPL Bioprinter N2+ with extrusion printing technology was used in this study. We delved into important design parameters of the fabricated bio-inks, including printing speed, infill percentage, printing trajectory, nozzle size, and extrusion pressure. Based on our findings, a printing speed of 550–750 mm/min is suitable for every bio-ink. The printing pressures for the NOCC-OXG range from 1.8 to 2 MPa, for NOCC-AHA from 0.5 to 0.7 MPa, for NOCC-AHA-Alg from 0.8 to 1 MPa, and for NOCC-AHA-OA from 1.3 to 1.6 MPa. Furthermore, the surface morphology of the bio-inks demonstrated a porous structure with a high degree of porosity, which can support the process of cell proliferation. The NOCC-OXG with 25G nozzle produced the most stable printed strands among different bio-ink systems. The results also exhibited that the compression strength of the NOCC-OXG gel system was 31–37 kPa, which is suitable for hard tissue. On the other hand, the NOCC-AHA-OA gel system is appropriate for fabricating more elastic tissue with compression stress of 10–18 kPa. Overall, these findings provide valuable insights for future biomedical research.