You are both there to workout, so theres no harm in saying lets do it together? Tease her saying you'll run your sessions like military camp! Then actually turn up with a brown and green stripe on each cheek (you dont have to do that, but i usually take things that far for fun)
Tell her you can teach her a few things to get the results she wants (then quickly grab a personal trainer book lol)
Go to the gym with her twice, the second time stay for a while after in the restaurant and grab some lunch. At the end of the lunch tell her what exciting stuff your up to on the weekend and she should come along.
If she cant make it, repeat the process but just do something different in stead of grab lunch, go for a milkshake or something. Keep moving the boundary from gym buddies to grabbing lunch to going to the mall for milkshake until you actually are just hanging out together outside of the gym.
Let me know how it goes,
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