Most Helpful Girl
Don't break up with her just for that. Talk to her about it. If she continues to ignore you for her phone, then walk away, but don't just leave without trying to fix things.
Most Helpful Guy
So what you do is go on about your business like you didn't even notice. She's on the phone, go out with friends, leave a note saying, hey wanted to go out but saw you on the phone. I'm out at XXXXX with my friends give me a call if you wanna join. If she starts giving you a hard time, tell her to get the fuck off the phone and she can join you in life.