In this work, dense, porous and, for the first time, functionally-graded bi-layer scaffolds with a cylindrical geometry were produced from a commercially available hydroxyapatite powder using the robocasting technique. The bi-layer scaffolds were made of a dense core part attached to a surrounding porous part. Subsequently, these bi-layer robocast scaffolds were joined with an outer shell of an antibacterial porous polymer layer fabricated by solvent casting/salt leaching techniques, leading to hybrid ceramic-polymer scaffolds. The antibacterial functionality was achieved through the addition of silver ions to the polymer layer. All the robocast samples, including the bi-layer ones, were first characterized through scanning electron microscopy observations, mechanical characterization in compression and preliminary bioactivity tests. Then, the hybrid bi-layer ceramic-polymer scaffolds were characterized through antimicrobial tests. After sintering at 1300 °C for 3 h, the compressive strengths of the structures were found to be equal to 29 ± 4 MPa for dense samples and 7 ± 4 MPa for lattice structures with a porosity of 34.1%. Bioactivity tests performed at 37 °C for 4 weeks showed that the precipitated layer on the robocast samples contained octacalcium phosphate. Finally, it was evidenced that the hybrid structure was effective in releasing antibacterial Ag+ ions to the surrounding medium showing its potential efficiency in limiting Staphylococcus aureus proliferation during surgery.