The reason I asked about the "alpha female" thing is that certain aspects of the behavior you are describing fits my most recent ex to a "t," she was exactly the "alpha female" type (on the surface at least), and that woman turned out to be the most disordered human being I've ever met. Always making it a point to let on how many men were flirting with her or desiring her. Mixed signals, nutty statements akin to the "wanting to stay single" comment she made to you. Be very very careful with this one. Best wishes.