Bioprinting allows for the fabrication of tissue-like constructs by precise architecture and positioning of the bioactive hydrogels with living cells. This study was performed to determine the effect of very low concentrations of alginate (0.1, 0.3, and 0.5% w/v) on bioprinting of bone marrow mesenchymal stem cells (BMSC) in gelatin methacryloyl (GelMA; 5% w/v)/alginate blend. Furthermore, while GelMA was photocrosslinked in all bioprinted constructs, the effect of crosslinking alginate with calcium chloride on the physical and biological characteristics of the constructs was investigated. The inclusion of low-concentration alginate improved the viscosity and printability of the formulation as well as the compressive modulus of the hydrogels, particularly when ionically crosslinked with calcium chloride, compared with the group in that alginate was not crosslinked. However, the stability and degradability of 3D printed scaffolds that were only photocrosslinked were comparable to those that were additionally crosslinked with calcium chloride. Noteworthily, ionic crosslinking of alginate deteriorated the viability of BMSC. Morphology and growth of BMSC were improved by adding a low alginate concentration; however, ionic crosslinking of alginate affected these factors adversely. The findings of this study underscore the significance of carefully evaluating the crosslinking strategy used in conjunction with cell-laden GelMA/alginate hydrogel to achieve balanced physical and biological properties as well as less complicated post-bioprinting processing.