The gif below shows Noriko from minute 11 of GunBuster's episode 3.
This is the dialogue directly preceding it:
Noriko: I should at least memorize basic space manoeuvring patterns. [...]
Smith: All that stuff is useless in real combat.
Noriko: Why do you have to keep patronizing me?
Smith: 'cause your such a cute little freshman.
Noriko: I'll have you know that Onee-sama and I are the best team in the entire Top Squadron! A "solo" like you with no partner couldn't possibly appreciate everything we've been through together as a team. So long!
In terms of usage it seems somewhat interchangeable with the Eyelid pull taunt. I assumed it is meant to show defiance, kind of like baring one's teeth but in a more cheeky way?
The sound she makes is "bi-" I would say, but her action doesn't really fit any of the common uses of that onomatopoeia which I'm aware of.
So, TL;DR, does this have a name, is it repeated throughout anime and signifies something particular or is it just Noriko being random and I'm overthinking it?