Centella asiatica, propolis, and hinokitiol, as natural antibacterial reagents, were integrated into the poly[(R)-3-hydroxybutyrate-co-(R)-3-hydroxyhexanoate] (PHBH) polymer to produce antibacterial wound dressings, using electrospinning process. The results showed that the fiber diameters and surface morphology of PHBH composite nanofibers were influenced by the addition of ethanol–centella (EC), methanol–centella (MC), ethanol–propolis (EP), and ethanol–hinokitiol (EH) at various ratios compared to pristine PHBH nanofibers. From FT-IR, the nanofibrous samples with higher contents of natural antibacterial substances showed the peaks of carboxylic acid, aromatic ring, and tropolone carbon ring from centella, propolis, and hinokitiol, respectively. Furthermore, the tensile strength of neat PHBH nanofibers was increased from 8.00 ± 0.71 MPa up to 16.35 ± 1.78 MPa by loading of propolis (EP) 7% into PHBH. X-ray analysis explained that the loading of propolis (EP) was also able to increase the crystallinity in PHBH composite nanofibers from 47.0% to 54.5%. The antibacterial results demonstrated that PHBH composite nanofibers containing natural antibacterial products were potent inhibitors against the growth of Escherichia coli and Staphylococcus aureus, amongst them hinokitiol and propolis proved to be the most effective. Additionally, the release studies displayed that centella and hinokitiol had faster release from PHBH composite nanofibers in comparison to propolis.