This study investigates how varying concentrations of hydroxyapatite (OHAp) and the addition of gelatin influence the ionic crosslinking time of alginate-based bioinks, as well as the shear stress experienced by neonatal human dermal fibroblasts (HDFn) during extrusion. These factors are crucial for validating bioinks and developing viable 3D bioprinted models. Four bioink formulations were created with a 50/50 ratio of alginate to gelatin, incorporating different calcium phosphate concentrations (0%, 1%, 5%, and 10%). The bioink compositions were confirmed via Fourier Transform Infrared (FT-IR) spectroscopy, and rheological analyses evaluated their pseudoplastic behavior, printability limits, and crosslinking times. The results indicated a notable increase in the consistency index (k) from 0.32 for the 0% OHAp formulation to 0.48 for the 10% OHAp formulation, suggesting improved viscoelastic properties. The elastic modulus recovery after crosslinking rose significantly from 245 Pa to 455 Pa. HDFn experienced a shear stress of up to 1.5436 Pa at the tip during extrusion with the HDFn-ALG5-GEL5-OHAp10 bioinks, calculated at a shear rate as low as 2 s