Hairy root cultures are valuable sources of a range of phytochemicals. Among them, Salvia bulleyana root culture is a promising source of polyphenols, especially rosmarinic acid (RA), a phenolic acid depside with pleiotropic activity and a wide application in medicine and cosmetology. The aim of the study was to enhance the culture productivity by finding suitable elicitation protocol and to determine its biological potential in terms of antioxidant, anticancer and antimicrobial properties. The total content of phenols and the levels of particular constituents in root extracts were analyzed using HPLC-PDA. Among four elicitors tested (yeast extract; methyl jasmonate, MJA; trans-anethol; and cadmium chloride), MJA was found to be the most effective. The greatest boost in phenolic production (up to 124.4 mg/g dry weight) was observed after three-day treatment with MJA at 100 µM, with an almost 100% improvement compared to the controls (non-treated root culture). The hydromethanolic extract from the elicited culture exhibited strong antioxidant activity with IC50 values of 11.1 µg/mL, 6.5 µg/mL and 69.5 µg/mL for DPPH (2,2-diphenyl-1-picrylhydrazyl), ABTS (2,2-azinobis-(3-ethylbenzthiazoline-6-sulfonic acid)) and superoxide anion radical, respectively. Moreover, in concentrations of 0.5–5 mg/mL the extract inhibited the growth of LoVo, AGS and HeLa cell lines, but was safe for the L929 cells up to the concentration of 5 mg/mL. The extract also exhibited moderate antimicrobial activity. Thus, the results confirmed that elicitation can be a beneficial strategy for increase the phenolic acid biosynthesis in hairy roots of S. bulleyana, and that such a highly productive culture can show significant biological potential.