Catalyzes the 2-thiolation of uridine at the wobble position (U34) of tRNA, leading to the formation of s(2)U34. AH2 + ATP + S-sulfanyl-L-cysteinyl-[protein] + uridine(34) in tRNA = 2-thiouridine(34) in tRNA + A + AMP + diphosphate + H(+) + L-cysteinyl-[protein] Belongs to the MnmA/TRMU family.