Catalysis of the reaction: 5,10-methylenetetrahydrofolate + tRNA containing uridine at position 54 + FADH + H+ = tetrahydrofolate + tRNA containing ribothymidine at position 54 + FAD+.
tRNA (uracil(54)-C(5))-methyltransferase activity, 5,10-methylenetetrahydrofolate-dependent