The increasing demand for novel tissue engineering (TE) applications in bone tissue regeneration underscores the importance of exploring advanced manufacturing techniques and biomaterials for personalised treatment approaches. Three-dimensional printing (3DP) technology facilitates the development of implantable devices with intricate geometries, enabling patient-specific therapeutic solutions. Although Fused Filament Fabrication (FFF) and Direct Ink Writing (DIW) are widely utilised for fabricating bone-like implants, the need for multiple processing steps often prolongs the overall production time. In this study, a single-step melt-extrusion 3DP technique was performed to develop multi-material scaffolds including bioceramics, hydroxyapatite (HA), and β-tricalcium phosphate (TCP) in both their bioactive and calcined forms at 10% and 20% w/w, within polycaprolactone (PCL) matrices. Printing parameters were optimised, and physicochemical properties of all biomaterials and final forms were evaluated. Thermal degradation and surface morphology analyses assessed the consistency and distribution of the ceramics across the different formulations. The tensile testing of the scaffolds defined the impact of each ceramic type and wt% on scaffold flexibility performance, while in vitro cell studies determined the cytocompatibility efficiency. Hence, all 3D-printed PCL–ceramic composite scaffolds achieved structural integrity and physicochemical and thermal stability. The mechanical profile of extruded samples was relevant to the ceramic consistency, providing valuable insights for further mechanotransduction investigations. Notably, all materials showed high cell viability and proliferation, indicating strong biocompatibility. Therefore, this additive manufacturing (AM) process is a precise and fast approach for developing biomaterial-based scaffolds, with potential applications in surgical restoration and support of segmental bone defects.