In the presented work, poly(3-hydroxybutyrate)–PHB-based composite blends for bone medical applications and tissue engineering are prepared and characterized. PHB used for the work was in two cases commercial and, in one case, was extracted by the chloroform-free route. PHB was then blended with poly(lactic acid) (PLA) or polycaprolactone (PCL) and plasticized by oligomeric adipate ester (Syncroflex, SN). Tricalcium phosphate (TCP) particles were used as a bioactive filler. Prepared polymer blends were processed into the form of 3D printing filaments. The samples for all the tests performed were prepared by FDM 3D printing or compression molding. Differential scanning calorimetry was conducted to evaluate the thermal properties, followed by optimization of printing temperature by temperature tower test and determination of warping coefficient. Tensile test, three-point flexural test, and compression test were performed to study the mechanical properties of materials. Optical contact angle measurement was conducted to determine the surface properties of these blends and their influence on cell adhesion. Cytotoxicity measurement of prepared blends was conducted to find out whether the prepared materials were non-cytotoxic. The best temperatures for 3D printing were 195/190, 195/175, and 195/165 °C for PHB-soap/PLA-SN, PHB/PCL-SN, and PHB/PCL-SN-TCP, respectively. Their mechanical properties (strengths ~40 MPa, moduli ~2.5 GPa) were comparable with human trabecular bone. The calculated surface energies of all blends were ~40 mN/m. Unfortunately, only two out of three materials were proven to be non-cytotoxic (both PHB/PCL blends).