It is clear you are going to try and talk to her in spite of the unanimous opinion that this is a bad idea. So, go ahead and do it ... at your own risk.
No one cay whether an apology will be considered stalking or some other crime. A lot depends on the nature of the alleged "apology." If you follow her, track her down, and confront her in a public place, maybe it will. If you send a letter with a short sentence saying, "I'm sorry for being a jerk and I will never speak with you again - best wishes for a wonderful life," and that's it - maybe it won't. The specifics of the contact and how it makes her feel when coupled with any past contacts will be part of any evaluation as to any criminal acts.
If you are fishing for someone to give you a clearly black or white decision, you ain't gonna find it. Since you seem intent on continuing this infatuation, I can only predict that this will not end well. This time it's an apology, next time it will be an explanation, the time after that another apology, and so on ... I've put people like that in prison. You'd best beware that your actions CAN be seen as threatening, and at the very least, creepy. Move on, get therapy, and focus on your business venture.
