Medical nutrients obtained from plants have been used in traditional medicine since ancient times, owning to the protective and therapeutic properties of plant extracts and products. Glycyrrhizic acid is one of those that, apart from its therapeutic effect, may contribute to stronger bones, inhibiting bone resorption and improving the bone structure and biomechanical strength. In the present study, we investigated the effect of a bioactive glass (BG) addition to the structure–property relationships of supramolecular assemblies formed by glycyrrhizic acid (GA) and its monoammonium salt (MSGA). FTIR spectra of supramolecular assemblies evidenced an interaction between BG components and hydroxyl groups of MSGA and GA. Moreover, it was revealed that BG components may interact and bond to the carboxyl groups of MSGA. In order to assess their biological effects, BG, MSGA, and their supramolecular assemblies were introduced to a culture of human bone-marrow-derived mesenchymal stromal cells (BMSCs). Both the BG and MSGA had positive influence on BMSC growth, viability, and osteogenic differentiation—these positive effects were most pronounced when BG1d-BG and MSGA were introduced together into cell culture in the form of MSGA:BG assemblies. In conclusion, MSGA:BG assemblies revealed a promising potential as a candidate material intended for application in bone defect reconstruction and bone tissue engineering approaches.