Tissue engineering is a current trend in the regenerative medicine putting pressure on scientists to develop highly functional materials and methods for scaffolds’ preparation. In this paper, the calibrated filaments for Fused Deposition Modeling (FDM) based on plasticized poly(3-hydroxybutyrate)/poly(d,l-lactide) 70/30 blend modified with tricalcium phosphate bioceramics were prepared. Two different plasticizers, Citroflex (n-Butyryl tri-n-hexyl citrate) and Syncroflex (oligomeric adipate ester), both used in the amount of 12 wt%, were compared. The printing parameters for these materials were optimized and the printability was evaluated by recently published warping test. The samples were studied with respect to their thermal and mechanical properties, followed by biological in vitro tests including proliferation, viability, and osteogenic differentiation of human mesenchymal stem cells. According to the results from differential scanning calorimetry and tensile measurements, the Citroflex-based plasticizer showed very good softening effect at the expense of worse printability and unsatisfactory performance during biological testing. On the other hand, the samples with Syncroflex demonstrated lower warping tendency compared to commercial polylactide filament with the warping coefficient one third lower. Moreover, the Syncroflex-based samples exhibited the non-cytotoxicity and promising biocompatibility.