My best advice would be to sit down and talk to this girl one on one, just you and her. Put aside looks, put aside first impressions, put it all aside. Sometimes people try so hard during rush because they don't know how else to act. If you make the effort to talk to her and get to know beyond what is physically there, perhaps you will see that this girl could be a real asset to your organization.
In all honesty, I know you are worried about the future of your organization, but you don't have that much control over that. Even the girls that seem to be the most like you can have completely different opinions on the growth of the sorority. Think about the here and now. While you are still active, do you think that this girl would be a contribution to your organization and that your organization would be a benefit to her? That's the real issue.
If you start there, then the rest should fall into place. She might not be someone to bid, but you don't know that unless you make that effort.
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