A girlfriend I've been with on and off doesn't counter propose a date to meet at my place but rather makes excuses not to come, even when she is proposed to come on my expenses be it for the gas, ride or a public transport. She doesn't mind meeting in public and showing me off to friends, is affectionate when we hang alone out and on the flipside barely when in front of her female friends, almost masculine. I work, she doesn't, I have options and she knows she's replacable (on and off relatoonship).

I can never close her on coming to my place.

What do you call this and how do you proceed with this kind of chick?