Biodegradable composite materials represent one of the major areas of investigation for bone tissue engineering due to their tuneable compositional and mechanical properties, which can potentially mimic those of bone and potentially avoid the removal of implants, mitigating the risks for the patient and reducing the overall clinical costs. In addition, the introduction of additive manufacturing technologies enables a strict control over the final morphological features of the scaffolds. In this scenario, the optimisation of 3D printable resorbable composites, made of biocompatible polymers and osteoinductive inorganic phases, offers the potential to produce a chemically and structurally biomimetic implant, which will resorb over time. The present work focuses on the development and process optimisation of two hybrid composite filaments, to be used as feedstock for the fused filament fabrication 3D printing process. A Poly L-lactic acid matrix was blended with either rod-like nano-hydroxyapatite (nano-HA) or nanoparticles of mesoporous bioactive glasses, both partially substituted with strontium (Sr2+), due to the well-known pro-osteogenic effect of this ion. Both inorganic phases were incorporated into Poly L-lactic acid using an innovative combination of processes, obtaining a homogeneous distribution throughout the polymer whilst preserving their ability to release Sr2+. The filament mechanical properties were not hindered after the incorporation of the inorganic phases, resulting in tensile strengths and moduli within the range of cancellous bone, 50 ± 10 MPa and 3 ± 1 GPa. Finally, the rheological characterization of the hybrid composites indicated a shear thinning behaviour, ideal for the processing with fused filament fabrication, proving the potential of these materials to be processed into 3D structures aiming bone regeneration.