Bone tissue is the second tissue to be replaced. Annually, over four million surgical treatments are performed. Tissue engineering constitutes an alternative to autologous grafts. Its application requires three-dimensional scaffolds, which mimic human body environment. Bone tissue has a highly organized structure and contains mostly inorganic components. The scaffolds of the latest generation should not only be biocompatible but also promote osteoconduction. Poly (lactic acid) nanofibers are commonly used for this purpose; however, they lack bioactivity and do not provide good cell adhesion. Chitosan is a commonly used biopolymer which positively affects osteoblasts’ behavior. The aim of this article was to prepare novel hybrid 3D scaffolds containing nanohydroxyapatite capable of cell-response stimulation. The matrixes were successfully obtained by PLA electrospinning and microwave-assisted chitosan crosslinking, followed by doping with three types of metallic nanoparticles (Au, Pt, and TiO2). The products and semi-components were characterized over their physicochemical properties, such as chemical structure, crystallinity, and swelling degree. Nanoparticles’ and ready biomaterials’ morphologies were investigated by SEM and TEM methods. Finally, the scaffolds were studied over bioactivity on MG-63 and effect on current-stimulated biomineralization. Obtained results confirmed preparation of tunable biomimicking matrixes which may be used as a promising tool for bone-tissue engineering.