There are items called 'Bomb Queen Ash' and 'Bomb Queen Core' floating around in people's bazaars on Siren.
I can't be 100% sure she really drops them, since according to a .jp website, to get her to spawn you must trade either 3 Bomb Queen Ashes or 1 Bomb Queen Core to a ??? in Ifrit's cauldron to spawn her.
This doesn't absolutely mean she doesn't drop them, but something else might.