In this work, we investigated, for the first time, the possibility of developing scaffolds for bone tissue engineering through three-dimensional (3D) melt-extrusion printing of medium chain length polyhydroxyalkanoate (mcl-PHA) (i.e., poly(3-hydroxyoctanoate-co-hydroxydecanoate-co-hydroxydodecanoate), P(3HO-co-3HD-co-3HDD)). The process parameters were successfully optimized to produce well-defined and reproducible 3D P(3HO-co-3HD-co-3HDD) scaffolds, showing high cell viability (100%) toward both undifferentiated and differentiated MC3T3-E1 cells. To introduce antibacterial features in the developed scaffolds, two strategies were investigated. For the first strategy, P(3HO-co-3HD-co-3HDD) was combined with PHAs containing thioester groups in their side chains (i.e., PHACOS), inherently antibacterial PHAs. The 3D blend scaffolds were able to induce a 70% reduction of Staphylococcus aureus 6538P cells by direct contact testing, confirming their antibacterial properties. Additionally, the scaffolds were able to support the growth of MC3T3-E1 cells, showing the potential for bone regeneration. For the second strategy, composite materials were produced by the combination of P(3HO-co-3HD-co-HDD) with a novel antibacterial hydroxyapatite doped with selenium and strontium ions (Se-Sr-HA). The composite material with 10 wt % Se-Sr-HA as a filler showed high antibacterial activity against both Gram-positive (S. aureus 6538P) and Gram-negative bacteria (Escherichia coli 8739), through a dual mechanism: by direct contact (inducing 80% reduction of both bacterial strains) and through the release of active ions (leading to a 54% bacterial cell count reduction for S. aureus 6538P and 30% for E. coli 8739 after 24 h). Moreover, the composite scaffolds showed high viability of MC3T3-E1 cells through both indirect and direct testing, showing promising results for their application in bone tissue engineering.