How to initiate conversation with this girl?

Ok so here is the scoop. About 6 months ago I had to go to physical therapy for a while for an injury. My therapist was really cool, we talked about anything but therapy – she is about my same age (mid-20s). I know her job is to be nice and caring but I feel like we had some sort of bond that was more than that.

Maybe 2 months after I finished therapy she added me on LinkedIn (I know this story is sounding so internet cheesy), but we never said anything to eachother – every now and then she will view my profile so I can’t help but think maybe she thinks about me too.

I could be entirely wrong and be making this into something its not, but I’d like to write her a message of some sort just to say hello and maybe feel her out to see if she would be interested in hanging out at some point.

The problem is that I don’t know what to say, I don’t want her to wonder why I would try to contact her or think I’m weird or anything, but I don’t really have anything to lose as we don’t talk now. Can you guys help me figure out something to say to her??