Many thermoelectrics such as Bi exhibit Rashba spin-orbit surface bands for which topological insulator behavior consisting of ultrahigh mobilities and enhanced thermopower has been predicted. Bi nanowires realize surface-only electronic transport since they become bulk insulators when they undergo the bulk semimetal-semiconductor transition as a result of quantum confinement for diameters close to 50 nm. We studied 20, 30, 50, and 200 nm trigonal Bi wires. Shubnikov-de Haas magnetoresistance oscillations caused by surface electrons and bulklike holes enable the determination of their densities and mobilities. Surface electrons have high mobilities exceeding 2 m2 sec^-1 V ^-1 and contribute strongly to the thermopower, dominating for temperatures T < 100 K. The surface thermopower is -1.2 T μV/K2, a value that is consistent with theory, raising the prospect of developing nanoscale thermoelectrics based on surface bands.