Nanostructured composites and nanowire arrays of traditional thermoelectrics like Bi, Bi_1-xSb_x and Bi ₂Te₃ have metallic Rashba surface spin-orbit bands featuring high mobilities rivaling that of the bulk, for which topological insulator behavior has been proposed. Nearly pure surface electronic transport has been observed at low temperatures in Bi nanowires with diameter around the critical diameter, 50 nm, for the semimetal-to semiconductor transition. The surface contributes strongly to the thermopower, actually dominating for temperatures T < 100 K in these nanowires. The surface thermopower was found to be-1 T μV/K², a value that is consistent with theory. We show that surface electronic transport together with boundary phonon scattering leads to enhanced thermoelectric performance at low temperatures of Bi nanowire arrays. We compare with bulk n-BiSb alloys, optimized CsBi₄Te ₆ and optimized Bi₂Te₃. Surface dominated electronic transport can be expected in nanomaterials of the other traditional thermoelectrics.