How do i go about talking to her after bad first impression?

im 16 and a junior she's a freshman 14 and i sort of have a crush on her shes cute and baby-faced and asian if that matters. ok so yeah i see her in the morning when i come in, during my lunch period, and we both get out the same period( not to sound creepy or stalkerish). A while back i made a bad impression, first of all she used to have a winne the pooh bag now she doesn't maybe because of me, so me thinking it would be playful or cute i tried to talk to her calling her winnie the pooh during lunch but then i realized i was being a jerk so i was going to say sorry so i walked up to her table sat down look her in the face then i saw her face then i froze then i left ( i know right) so yea that was embarring and just made it awkward . Since then every time i p there little freshman table they all stare at me and start talking ( i hate that because i never know what they say). just today i had to wait to go to the bathroom and i sat at the table next to theirs and they were talking about me i couldn't make out what they were saying except that's the guy. But yeah how should i approach next time i see her? should i just say sorry for being a jerk or should i just introduce myself? should i be her friend first and just progress from there or just ask her out? How should i go about it? thank you, sorry for my long question