What to do about my ex?

my ex gf of a year broke up w/ me bc apparently i pressured her. i love her with all my heart,but its very hard to get her to realize tht sumtimes. at school she claimed and also told me after a while we could be friends and nothing more,ever.then soon after tht she told every1 she hated me and ***** even be my friend.well,now it's summertime. were talking.to my surprise,i asked her to the movies and she said yes,but just as friends. we text constantly thru the summer when we dont have work,etc. i dont wnt to ruin the friendship by asking for another chance, but i want to prove to her tht im different from those other guys. how do i go about doing this without making it obvious thts what i want to do?how can i get it out of her possibly without it being a straightforward ? tht would ruin everything?help!