tRNA (uracil-O(2)-)-methyltransferase, which catalyzes the formation of O(2)-methyluracil at position 44 (Um44) in tRNA(Ser). S-adenosyl-L-methionine + uridine(44) in tRNA(Ser) = 2'-O-methyluridine(44) in tRNA(Ser) + H(+) + S-adenosyl-L-homocysteine Present with 7720 molecules/cell in log phase SD medium. Belongs to the TRM44 family.