Over the years, essential oils (EOs) and their compounds have gained growing interest due to their anti-inflammatory, antimicrobial, antioxidant, and immunomodulatory properties. The aim of this study was to evaluate the effect of eight commercially available EO-derived compounds ((R)-(+)-limonene, (S)-(−)-limonene, sabinene, carvacrol, thymol, alpha-pinene (α-pinene), beta-pinene (β-pinene), and cinnamaldehyde) on the bone formation process in vitro to select the most promising natural agents that could potentially be used in the prevention or treatment of osteoporosis. Within this study, evaluation of cytotoxicity, cell proliferation, and osteogenic differentiation was performed with the use of mouse primary calvarial preosteoblasts (MC3T3-E1). Moreover, extracellular matrix (ECM) mineralization was determined using MC3T3-E1 cells and dog adipose tissue-derived mesenchymal stem cells (ADSCs). The two highest non-toxic concentrations of each of the compounds were selected and used for testing other activities. The conducted study showed that cinnamaldehyde, thymol, and (R)-(+)-limonene significantly stimulated cell proliferation. In the case of cinnamaldehyde, the doubling time (DT) for MC3T3-E1 cells was significantly shortened to approx. 27 h compared to the control cells (DT = 38 h). In turn, cinnamaldehyde, carvacrol, (R)-(+)-limonene, (S)-(−)-limonene, sabinene, and α-pinene exhibited positive effects on either the synthesis of bone ECM or/and mineral deposition in ECM of the cells. Based on the conducted research, it can be assumed that cinnamaldehyde and (R)-(+)-limonene are the most promising among all tested EO-derived compounds and can be selected for further detailed research in order to confirm their biomedical potential in the chemoprevention or treatment of osteoporosis since they not only accelerated the proliferation of preosteoblasts, but also significantly enhanced osteocalcin (OC) synthesis by preosteoblasts (the OC level was approx. 1100–1200 ng/mg compared to approx. 650 ng/mg in control cells) and ECM calcification of both preosteoblasts and mesenchymal stem cells. Importantly, cinnamaldehyde treatment led to a three-fold increase in the mineral deposition in ADSCs, whereas (R)-(+)-limonene caused a two-fold increase in the ECM mineralization of both MC3T3-E1 cells and ADSCs.