Increasing the demand for bone substitutes in the management of bone fractures, including osteoporotic fractures, makes bone tissue engineering (BTE) an ideal strategy for solving the constant shortage of bone grafts. Electrospun-based scaffolds have gained popularity in BTE because of their unique features, such as high porosity, a large surface-area-to-volume ratio, and their structural similarity to the native bone extracellular matrix (ECM). To imitate native bone mineralization through which bone minerals are deposited onto the bone matrix, a simple but robust post-treatment using a simulated body fluid (SBF) has been employed, thereby improving the osteogenic potential of these synthetic bone grafts. This study highlights recent electrospinning technologies that are helpful in creating more bone-like scaffolds, and addresses the progress of SBF development. Biomineralized electrospun bone scaffolds are also reviewed, based on the importance of bone mineralization in bone regeneration. This review summarizes the potential of SBF treatments for conferring the biphasic features of native bone ECM architectures onto electrospun-based bone scaffolds.