Direct ink writing (DIW) enables patient-specific fabrication of multifunctional bone scaffolds, but formulating inks that combine ceramic osteoconductivity, magnetic hyperthermia capability, and controlled drug delivery while retaining printability remains challenging. This study investigates the composition-dependent rheology and printability of polycaprolactone (PCL)/β-tricalcium phosphate (β-TCP)/magnetite (Fe₃O₄) colloidal gels (formulated inks) for DIW-based scaffold fabrication. Five formulations spanning 10–50 wt% PCL (with β-TCP adjusted accordingly and Fe₃O₄ fixed at 5 wt%) were synthesized via solvent-based gel casting, characterized, and evaluated rheologically (flow sweep, amplitude and frequency sweeps, three-interval thixotropy, gelation kinetics). All inks exhibited shear-thinning behavior. Intermediate PCL compositions showed higher storage moduli, broader linear viscoelastic regions, higher yield stress, and rapid post-shear recovery, indicative of well-percolated particle–polymer networks, while high-ceramic-loaded formulations displayed brittle behavior. Calculated yield pressures for intermediate compositions fell within practical DIW operating ranges. Printing tests confirmed that only intermediate solid loadings are reliably printed through both nozzle diameters, demonstrating that printability depends jointly on yield stress and solid fraction. These findings establish composition-based guidelines for optimizing multifunctional PCL/β-TCP/Fe₃O₄ inks toward printable, patient-specific bone scaffolds.