Inorganic–organic hybrid biomaterials have been proposed for bone tissue repair, with improved mechanical flexibility compared with scaffolds fabricated from bioceramics. However, obtaining hybrids with osteoinductive properties equivalent to those of bioceramics is still a challenge. In this work, we present for the first time the synthesis of a class II hybrid modified with bioactive glass nanoparticles (nBGs) with osteoinductive properties. The nanocomposite hybrids were produced by incorporating nBGs in situ into a polytetrahydrofuran (PTHF) and silica (SiO2) hybrid synthesis mixture using a combined sol–gel and cationic polymerization method. nBGs ~80 nm in size were synthesized using the sol–gel technique. The structure, composition, morphology, and mechanical properties of the resulting materials were characterized using ATR-FTIR, 29Si MAS NMR, SEM-EDX, AFM, TGA, DSC, mechanical, and DMA testing. The in vitro bioactivity and degradability of the hybrids were assessed in simulated body fluid (SBF) and PBS, respectively. Cytocompatibility with mesenchymal stem cells was assessed using MTS and cell adhesion assays. Osteogenic differentiation was determined using the alkaline phosphatase activity (ALP), as well as the gene expression of Runx2 and Osterix markers. Hybrids loaded with 5, 10, and 15% of nBGs retained the mechanical flexibility of the PTHF–SiO2 matrix and improved its ability to promote the formation of bone-like apatite in SBF. The nBGs did not impair cell viability, increased the ALP activity, and upregulated the expression of Runx2 and Osterix. These results demonstrate that nBGs are an effective osteoinductive nanoadditive for the production of class II hybrid materials with enhanced properties for bone tissue regeneration.