i dont think you should try and talk to her. you have to remember that even if your intentions are pure, you never know what might happened
the prophet said that if two people (different gender) were together alone talking the shaytaan is always the third person
so keep it safe and talk to her mahram
what you are doing, by lowering your gaze that is, is very important and the right way. Keep it up bro
I pray inshallah Allah make things easier for you
