Transformed shoots of the Tibetan medicinal plant Dracocephalum forrestii were cultured in temporary immersion bioreactors (RITA and Plantform) and in nutrient sprinkle bioreactor (NSB) for 3 weeks in MS (Murashige and Skoog) liquid medium with 0.5 mg/L BPA (N-benzyl-9-(2-tetrahydropyranyl)-adenine) and 0.2 mg/L IAA (indole-3-acetic acid). The greatest biomass growth index (GI = 52.06 fresh weight (FW) and 55.67 dry weight (DW)) was observed for shoots in the RITA bioreactor, while the highest multiplication rate was found in the NSB (838 shoots per bioreactor). The levels of three phenolic acids and five flavonoid derivatives in the shoot hydromethanolic extract were evaluated using UHPLC (ultra-high performance liquid chromatography). The predominant metabolite was rosmarinic acid (RA)—the highest RA level (18.35 mg/g DW) and total evaluated phenol content (24.15 mg/g DW) were observed in shoots grown in NSB. The NSB culture, i.e., the most productive one, was evaluated for its antioxidant activity on the basis of reduction of ferric ions (ferric reducing antioxidant power, FRAP) and two scavenging radical (O₂^•– and DPPH, 1,1-diphenyl-2-picrylhydrazyl radical) assays; its antibacterial, antifungal, and antiproliative potential against L929 cells was also tested (3-[4,5-dimethylthiazole-2-yl]-2,5-diphenyltetrazolium bromide (MTT) test). The plant material revealed moderate antioxidant and antimicrobial activities and demonstrated high safety in the MTT test—no cytotoxicity at concentrations up to 50 mg/mL was found, and less than a 20% decrease in L929 cell viability was observed at this concentration.