I think "babushka" is a metaphor, meaning the kind of hat a Russian grandmother used to wear,
being a diminutive of 'baba: as in "Baba Yaga".
babushka
n.
5Russ, grandmother, dim. of baba, old woman, orig. < baby talk: so named as frequent garb of old women6 a kerchief or scarf worn on the head by a woman or girl and tied under the chin