The microarchitecture of bone tissue engineering (BTE) scaffolds has been shown to have a direct effect on the osteogenesis of mesenchymal stem cells (MSCs) and bone tissue regeneration. Poly(glycerol sebacate) (PGS) is a promising polymer that can be tailored to have specific mechanical properties, as well as be used to create microenvironments that are relevant in the context of BTE applications. In this study, we utilized PGS elastomer for the fabrication of a biocompatible and bioactive scaffold for BTE, with tissue-specific cues and a suitable microstructure for the osteogenic lineage commitment of MSCs. In order to achieve this, the PGS was functionalized with a decellularized bone (deB) extracellular matrix (ECM) (14% and 28% by weight) to enhance its osteoinductive potential. Two different pore sizes were fabricated (small: 100–150 μm and large: 250–355 μm) to determine a preferred pore size for in vitro osteogenesis. The decellularized bone ECM functionalization of the PGS not only improved initial cell attachment and osteogenesis but also enhanced the mechanical strength of the scaffold by up to 165 kPa. Furthermore, the constructs were also successfully tailored with an enhanced degradation rate/pH change and wettability. The highest bone-inserted small-pore scaffold had a 12% endpoint weight loss, and the pH was measured at around 7.14. The in vitro osteogenic differentiation of the MSCs in the PGS-deB blends revealed a better lineage commitment of the small-pore-sized and 28% (w/w) bone-inserted scaffolds, as evidenced by calcium quantification, ALP expression, and alizarin red staining. This study demonstrates a suitable pore size and amount of decellularized bone ECM for osteoinduction via precisely tailored PGS elastomer BTE scaffolds.