Most Helpful Girl
Most Helpful Guy
Does she even smile when you approach her or talk to her? If not, then there's a 99% chance that she doesn't have any interest in you; she was probably just staring into empty space in your general direction. Girls sometimes do that. xD You can ask her why she stares, just to be sure though.
But if she's not interested, then no, your plan would NOT make her more interested. It will just make her forget all about you even faster. The average girl has many more options and many things calling for her attention, compared to the average guy in society. Unless a girl is interested in a guy, she barely notices him. So on top of that, if you remove your persistence/aggressiveness in pursuing her, a girl EASILY forgets that you ever existed.
You already said that she has a whole "meh" attitude during your conversations and she even literally walked away from you once, and she gives terse 1-word answers when you talk. Here's the thing, man: when a girl is really into a guy, she doesn't give terse answers, but makes an effort to really respond to you and keep things going. And if you call or message her, she doesn't "forget" to respond. Why? Because you'd be on her mind, so she can't forget.