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.