[Kevin]

Allow me to swerve into your lane a little bit. COBing is much more like the sort of recruitment fraternities do outside of your top schools where formal recruitment fills the roster. You might not want to be so direct until you learn her real reason for not rushing.

The NIC has a 5-step model for individual recruitment: 1) Meet [her]; 2) Make [her] a friend; 3) Introduce [her] to your friends; 4) Introduce [her] to your [sorority]; 5) Ask [her] to join.

It sounds like you're sort of in the middle of step 2. How you likely joined and how you're attempting to recruit this lady are two very different paths. She may not understand the benefits of Greek life, so as Louisa says, it's best if she just not know you're recruiting her at all. Don't bring up the whole sorority thing until she's had an opportunity to see and experience how your sorority has benefited you. You don't have to draw her a picture, she'll see it for herself. Once she's had that opportunity to see how it's benefited you and you've introduced her to a few of your sisters, then you can start addressing directly the benefits of Greek Life, give her a house tour, show her how it's so much better living in your sorority house than the dorms, then if your chapter is willing, let her know she's got a bid and close the deal.