Poly(propylene fumarate) (PPF) is a linear and unsaturated copolyester based on fumaric acid that has been widely investigated for tissue engineering applications in recent years due to its tailorable mechanical performance, adjustable biodegradability and exceptional biocompatibility. In order to improve its mechanical properties and spread its range of practical applications, novel approaches need to be developed such as the incorporation of fillers or polymer blending. Thus, PPF-based bionanocomposites reinforced with different amounts of single-walled carbon nanotubes (SWCNT), multi-walled carbon nanotubes (MWCNT), graphene oxide nanoribbons (GONR), graphite oxide nanoplatelets (GONP), polyethylene glycol-functionalized graphene oxide (PEG-GO), polyethylene glycol-grafted boron nitride nanotubes (PEG-g-BNNTs) and hydroxyapatite (HA) nanoparticles were synthesized via sonication and thermal curing, and their morphology, biodegradability, cytotoxicity, thermal, rheological, mechanical and antibacterial properties were investigated. An increase in the level of hydrophilicity, biodegradation rate, stiffness and strength was found upon increasing nanofiller loading. The nanocomposites retained enough rigidity and strength under physiological conditions to provide effective support for bone tissue formation, showed antibacterial activity against Gram-positive and Gram-negative bacteria, and did not induce toxicity on human dermal fibroblasts. These novel biomaterials demonstrate great potential to be used for bone tissue engineering applications.