In this paper, we present a new series of alkali‐free bioactive glasses (BG) based on FastOs^® composition (38.49 SiO₂ – 36.07 CaO – 19.24 MgO – 5.61 P₂O₅ – 0.59 CaF₂, expressed in mol %), which was modified by partially replacing silicon dioxide network‐former with boron trioxide network‐former, utilizing calcium oxide as a charge compensator. The main objective of this study was to obtain a new family of bioactive glasses suitable for the fabrication of glass fibers. The BGs were prepared by melt quenching technique and their structural and thermal properties were determined. Glass rods were used to obtain fibers by the classic drawing technique. The bioactivity of the fibers was subsequently assessed through immersion tests in simulated body fluid (SBF) to establish their ability to form hydroxyl carbonated (HCA) apatite onto their surfaces. Glasses with moderate substitution of SiO₂ with B₂O₃ exhibited enhanced thermal properties, allowing to significantly suppress the crystallization trend, and favoring to draw the fibers. The structure of the studied glasses was obtained by NMR spectroscopy. The structure‐property correlations were established by their relationship to the configurational entropy. Smaller amounts of substitution resulted in larger entropy of the glasses. Moreover the SBF tests revealed an extensive formation of HCA, comparable to the parent FastOs^®BG composition, which assures fast bonding to the bone. Thus, presented glass fibers may be considered as promising materials for wool‐like bone implants or as reinforcing constituent of biopolymer matrix composites.