The Trojan Horse Method was applied to the (2)H((6)Li, alpha(3)He)n three-body reaction in order to extract the bare nucleus S(E) factor for the 6Li(p, a)3 He reaction. The three-body reaction was performed in two kinematically complete experiments at beam energies of 25 and 14 MeV. The selected quasi-free coincidence yield was compared with the result of a Monte Carlo calculation where the entering two-body cross section was the result of a R-matrix parameterization of the direct two-body cross section. The quite good agreement throughout the investigated region above and below the p-(6)Li Coulomb barrier, allowed for the extraction of the bare S(E) factor in the astrophysical energy region. The S(0) value together with an independent estimate of the screening potential U(e) were derived and compared with those obtained from direct measurements.