Melt‐derived borate bioactive glass microfibers are showing a considerable capacity to heal chronic soft tissue wounds in humans and animals. In the present study, the degradation and conversion of borate (13‐93B3) bioactive glass microfibers (diameter = 0.2−5 microns) to hydroxyapatite (HA) in simulated body fluid (SBF) at 37 °C are studied and compared with the results for silicate 55S5 bioactive glass microfibers. The 13‐93B3 microfibers converted more rapidly to amorphous calcium phosphate (ACP) but crystallization of the ACP to HA appeared to occur more slowly when compared to the 45S5 microfibers. Doping the 13‐93B3 glass with CuO (0.4 wt. %) + ZnO (1.0 wt. %) or with CuO (0.4 wt. %) + ZnO (1.0 wt. %) + Fe2O3 (0.4 wt. %) + SrO (2.0 wt. %) had little effect on the degradation of microfibers and their conversion to ACP but it slowed the crystallization of the ACP to HA. The release of Cu and Sr ions from the doped microfibers into SBF is considerably higher than Zn and Fe ions which are mainly retained in the ACP or HA product. The results are relevant to the design of microfibrous bioactive glass with improved capacity for wound healing.