Bone tissue plays an important role in supporting and protecting the structure and function of the human body. Bone defects are a common source of injury and there are many reconstruction challenges in clinical practice. However, 3D bioprinting of scaffolds provides a promising solution. Hydrogels have emerged as biomaterials with good biocompatibility and are now widely used as cell-loaded materials for bioprinting. This study involved three steps: First, sodium alginate (SA), gelatin (Gel), and nano-hydroxyapatite (na-HA) were mixed into a hydrogel and its rheological properties assessed to identify the optimum slurry for printing. Second, SA/Gel/na-HA bioscaffolds were printed using 3D bioprinting technology and their physical properties characterized for surface morphology, swelling, and mechanical properties. Finally, human periodontal ligament stem cells (hPDLSCs) were mixed with SA/Gel/na-HA printing slurry to create a “bioink” to prepare SA/Gel/na-HA/ hPDLSCs cell bioscaffolds. These were tested for biocompatibility and osteogenic differentiation performance using live/dead cell staining, cell adhesion, cell proliferation, and alkaline phosphatase activity. The SA/Gel/na-HA hydrogel exhibited shear-thinning behavior. The equilibrium swelling of the bioscaffold was 125.9%, the compression stress was 0.671 MPa, and the compression elastic modulus was 8.27 MPa. The SA/Gel/na-HA/hPDLSCs cell bioscaffolds caused effective stimulation of cell survival, proliferation, and osteoblast differentiation. Therefore, the SA/Gel/na-HA/hPDLSCs cell bioscaffolds displayed potential as a material for bone defect reconstruction.