Hybrid scaffolds that are based on PLA and PLA/PMMA with 75/25, 50/50, and 25/75 weight ratios and functionalized with 10 wt.% of bioglass nanoparticles (n-BG) were developed using an electrospinning technique with a chloroform/dimethylformamide mixture in a 9:1 ratio for bone tissue engineering applications. Neat PLA and PLA/PMMA hybrid scaffolds were developed successfully through a (CF/DMF) solvent system, obtaining a random fiber deposition that generated a porous structure with pore interconnectivity. However, with the solvent system used, it was not possible to generate fibers in the case of the neat PMMA sample. With the increase in the amount of PMMA in PLA/PMMA ratios, the fiber diameter of hybrid scaffolds decreases, and the defects (beads) in the fiber structure increase; these beads are associated with a nanoparticle agglomeration, that could be related to a low interaction between n-BG and the polymer matrix. The Young’s modulus of PLA/PMMA/n-BG decreases by 34 and 80%, indicating more flexible behavior compared to neat PLA. The PLA/PMMA/n-BG scaffolds showed a bioactive property related to the presence of hydroxyapatite crystals in the fiber surface after 28 days of immersion in a Simulated Body Fluids solution (SBF). In addition, the hydrolytic degradation process of PLA/PMMA/n-BG, analyzed after 35 days of immersion in a phosphate-buffered saline solution (PBS), was less than that of the pure PLA. The in vitro analysis using an HBOF-1.19 cell line indicated that the PLA/PMMA/n-BG scaffold showed good cell viability and was able to promote cell proliferation after 7 days. On the other hand, the in vivo biocompatibility evaluated via a subdermal model in BALC male mice corroborated the good behavior of the scaffolds in avoiding the generation of a cytotoxic effect and being able to enhance the healing process, suggesting that the materials are suitable for potential applications in tissue engineering.