Biodegradable polymers and bioceramics give rise to composite structures that serve as scaffolds to promote tissue regeneration. The current research explores the preparation of biodegradable filaments for additive manufacturing. Bioresorbable segmented poly(ester urethanes) (SPEUs) are easily printable elastomers but lack bioactivity and present low elastic modulus, making them unsuitable for applications such as bone tissue engineering. Strategies such as blending and composite filament production still constitute an important challenge in addressing SPEU limitations. In this work, SPEU-poly(3-hydroxybutyrate-co-3-hydroxyvalerate) (PHBV) blends and SPEU-PHBV-Bioglass 45S5^® (BG) composite materials were processed into filaments and 3D structures. A comprehensive characterization of their morphology and thermal and mechanical properties is presented. The production of 3D structures based on SPEU-PHBV with excellent dimensional precision was achieved. Although SPEU-PHBV-BG printed structures showed some defects associated with the printing process, the physicochemical, thermal, and mechanical properties of these materials hold promise. The blend composition, BG content and particle size, processing parameters, and blending techniques were carefully managed to ensure that the mechanical behavior of the material remained under control. The incorporation of PHBV in SPEU-PHBV at 70:30 w/w and BG (5 wt%) acted as reinforcement, enhancing both the elastic modulus of the filaments and the compressive mechanical behavior of the 3D matrices. The compressive stress of the printed scaffold was found to be 1.48 ± 0.13 MPa, which is optimal for tissues such as human proximal tibial trabecular bone. Therefore, these materials show potential for use in the design and manufacture of customized structures for bone tissue engineering.