The release of therapeutic ions during dissolution is necessary for the success of bioactive glasses in medical applications. Therefore, different borate and borosilicate glasses undoped and doped with copper or/and zinc based on the 13–93 composition were tested and compared to the well-known 13–93 bioactive glass in several dissolution media. Prior to dissolution studies, all glasses were characterized using SEM-EDX, FTIR, XRD, DTA and hot stage microscopy (HSM). Dissolution studies were carried out using tris(hydroxymethyl)aminomethane (TRIS) buffer and simulated body fluid (SBF) under static conditions. The dissolution rates varied following the trend of borate glasses > borosilicate glasses > silicate glasses. Further, the release of boron from both borate and borosilicate glasses was inhibited in SBF compared to TRIS. The dissolution of the glasses was additionally tested in SBF under dynamic conditions to better mimic the human body environment. Under these conditions, Cu-doped glass released up to 10 mg/L of Cu2+, which is the critical biological level of Cu2+ for the survival of fibroblasts. In order to mimic the conditions that may develop locally during the degradation of a poly(lactic acid) (PLA) composite or during a bacterial infection, dissolution studies were for the first time also carried out using a lactic acid solution at pH = 2. Zinc was only released from the Zn-doped glasses under acidic conditions. Owing to the antibacterial property of Zn2+, these results are especially interesting for the application of the ion-doped glasses in the treatment or prevention of infections.