Unfortunately I am not a member of any groups of friends here. We are allowed 20 minutes for lunch, so going anywhere is pretty much a waste of valuable time. One has to drive all the out of the corporate park, then a half mile down a busy avenue for access to restaurants. We also do not work the same schedule. The end of her shift, is the middle of my shift.No letters on the car. That's creepy. Ask her to go to lunch with you and a group of friends from the office. This is easy, especially if there is a new place to go: "Hey, a bunch of us are going to check out Sal's Pizza tomorrow for lunch. Wanna go?"
My concern with intercepting her at the the exit is because I know her boss works 11hrs a day, and takes work home. I imagine she is putting in similar effort, since they leave at about the same time. I hope a letter through the mail isn't creepy. It appears to be the most effective way to communicate.