In short.. don't buy her shit and stay cool.
In other words...
+ Drop this asshole/sarcastic pose, it comes off tryhard to her so she thinks you're reacting to her therefore she's acting like a bitch to you. It's a lack of respect thing. Girls are turned off by weak behavior, once they smell it they become cruel simply because they can.
+ Play with your attention, turn with your body elsewhere, take away your attention when she does her snooty act, then look back if she's done with her shit, look at her like she's acting silly.
+ Command attention when you speak, speak slowly, almost lazily, make pauses to put some tension out.
+ Pay attention to your voice, breaking rapport tone is often necessary just to show you know what you're saying
+ Group dynamics and social proof is important, instead of working the girl, work the room/venue. When you talk to her invite others into your conversation if you can, let her see how other guys and girls like you and how you own them.
+ Non needy body language, lock in when you talk to her aka stand with the back to the wall and make her stand in front of you, not the other way around. Position yourself to make it look like it's her trying to talk to you even if it's not the case at first.
+ Do not take her seriously, treat her silly act accordingly, it's better to dismiss or roll eyes when she acts up instead of confronting her in direct manner to start verbal wars. You wouldn't try to reason with your little bratty sister. Stuck girls are no different.
+ End interactions on your terms whenever you want it. Can be even in the middle of your/her sentence, as if you noticed something/someone more interesting than her and her stupid pose. Then come back to her asking "so what was that you wanted from me again?" with silly smirk.
That's stuck up bitches management 101 off my memory. The whole point of those tips and tricks is to push you to the right state of mind and show her that she's not "all that" to you that she's thinking of herself. Once you're cool calm and confident you will do all those things naturally without thinking. That silly shit is just dumb and that's how you need to treat it.
It looks a little something like this, imagine she's the stuck up girl and cash is your game...