where does it all go?

In the manga and anime Demi-chan wa Kataritai the dullahan girl Kyouko had an invisible wormhole that food and beverages passed through. ZUN's never elaborated on Banki, but maybe it's the same.

Well...She's not a machine man.

I can only imagine Chen sliding that door slowly to the side, not once blinking or veering off her gaze from Banki´s head.
BLINK MOTHERFUCKER!

Chen's face when she open the door d'aaaaaaaaw.