Electrospinning is a versatile and straightforward technique to produce nanofibrous mats with different morphologies. In addition, by optimizing the solution, processing, and environmental parameters, three-dimensional (3D) nanofibrous scaffolds can also be created using this method. In this work, the preparation and characterization of bioactive glass (BG) scaffolds based on the SiO2–CaO sol–gel system, a biomaterial with a highly reactive surface, is reported. The electrospinning technique was combined with sol–gel methods to obtain nanofibrous 3D cotton wool-like scaffolds. The addition of zinc and copper ions to the silica-calcia system was examined, and the influence of these ions on the material properties and characteristics was investigated by various characterization techniques, from morphological and chemical properties to antibacterial and wound closure capability, cell viability and ion release. Our findings show that the cotton wool-like ion-doped nanofibers are promising for wound healing applications.