I think it's fine considering that it's a dialogue and not an essay. People don't always speak in perfect, grammatically correct sentences; therefore, it's okay to use colloquial language.

Don't start a sentence with "And." Also avoid "wanna." It's better to keep it flowing with a comma ("I heard you and Garrett making fun of my uncle in the library, and I don't want to speak to you.") Not now, not ever is better to say as "Not now or ever!" (The exclaimation point helps here).

This could be from a screen play (you may want to add notes on facial expression and gestures). BRYCE: Hi. You look nice. JULI: I heard you ... Garrett's making fun of my uncle in the library...and I don't wanna speak to you. Not now, not ever!

I agree with Cameron. Since, this is not an essay you don't have to worry about grammar issues. When we speak in English most of the time we don't speak in proper English, so don't worry it sounds good to me. ^^