S-adenosyl-L-methionine-dependent 2'-O-ribose methyltransferase that catalyzes the formation of 2'-O-methyluridine at position 1369 (Um1369) in the 16S mitochondrial large subunit ribosomal RNA (mtLSU rRNA), a universally conserved modification in the peptidyl transferase domain of the mtLSU rRNA. S-adenosyl-L-methionine + uridine(1369) in 16S rRNA = 2'-O-methyluridine(1369) in 16S rRNA + H(+) + S-adenosyl-L-homocysteine Belongs to the class I-like SAM-binding methyltransferase superfamily. RNA methyltransferase RlmE family.