A novel bioactive glass containing therapeutic ions with enhanced biocompatibility was designed and produced by the classical melt-quenching route. Starting from a very promising composition (Bio_MS), which combined bioactivity and high crystallization temperature, the ratio between some oxides was tailored to obtain a new and more reactive (in terms of dissolution rate) bioactive glass, called BGMSN (composition in mol%: 6.1 Na2O, 31.3 CaO, 5 MgO, 10 SrO, 2.6 P2O5, 45 SiO2). The aim of this work was to produce a bioactive glass with a good biological performance, preserving, at the same time, the high crystallization temperature achieved for Bio_MS; this is strategic in order to avoid undesired crystalline phases during thermal treatments, which can undermine the bioactivity and even the stability of final products. A complete characterization of the novel bioactive glass was performed in terms of thermal, mechanical and biological properties and in vitro bioactivity. The thermal behavior of the bioactive glass was studied by heating microscopy, differential thermal analysis (DTA) and optical dilatometry; BGMSN showed a very high crystallization temperature and a high sinterability parameter, thus being suitable for applications where thermal treatments are required, such as sintered samples, coatings and scaffolds. Mechanical properties were investigated by the micro-indentation technique. The in vitro biological properties were evaluated by means of both direct and indirect cell tests, i.e., neutral red (NR) uptake and MTT assay, using murine long bone osteocyte Y4 (MLO-Y4) cells: the cellular viability of BGMSN was higher compared to cellular viability of 45S5, both in direct and indirect tests. Finally, the in vitro bioactivity test by soaking samples in simulated body fluid (SBF) showed high dissolution rate, with a good rate of formation of hydroxyapatite.