Catalyzes the synthesis of dihydrouridine, a modified base found in the D-loop of most tRNAs. 5,6-dihydrouridine(20a) in tRNA + NADP(+) = H(+) + NADPH + uridine(20a) in tRNA 5,6-dihydrouridine(20a) in tRNA + NAD(+) = H(+) + NADH + uridine(20a) in tRNA 5,6-dihydrouridine(20b) in tRNA + NAD(+) = H(+) + NADH + uridine(20b) in tRNA 5,6-dihydrouridine(20b) in tRNA + NADP(+) = H(+) + NADPH + uridine(20b) in tRNA Belongs to the Dus family. Dus4 subfamily.