Catalyzes the 2'-O-methylation of the ribose of cytidine 1402 (C1402) in 16S rRNA. In vitro, active on the assembled 30S subunit, but not naked 16S rRNA or 70S ribosomes. cytidine(1402) in 16S rRNA + S-adenosyl-L-methionine = 2'-O-methylcytidine(1402) in 16S rRNA + H(+) + S-adenosyl-L-homocysteine Belongs to the methyltransferase superfamily. RsmI family.