It seems like she is currently torn between her feelings for you and the indoctrination she was submitted to growing up.
The reason she is acting that way is because JWs practice a form of isolationism, supposedly to protect themselves from "worldly influences" that might "lead them away from Jehovah." They view it as bad to have any friends who don't "love Jehovah." (which for them means being a baptized Witness, making all the meetings, going out in service, etc.) I'm not saying they won't be friendly with worldly people, but they won't typically spend any quality social time with you unless they can find a way to preach to you. That's probably why she seems so erratic, she wants to spend time with you, but when she does feels guilty.
The way I see it you have a few choices: you could try to convince her to leave behind the religious group again, but I'll be honest, your odds aren't good on that one. Perhaps if you could have an open discussion with her and tell her the changes you've noticed her behavior and how you're feeling things that'll do it, but she obviously went back to this group because she feels like she's missing something. (Most likely contact with her family.) Though if it is just "spirituality" that she seeks, you could use a resource like jwfacts.com to try and convince her that the JWs aren't the right place for that.Though once again, easier said than done you're probably facing off against over a decade of indoctrination into the JWs. (Note there is a strong possibility that she will call tha website "apostate" so I wouldn't share it as being the source of your info, might make her mad and unreceptive.)
You could start "studying the Bible" (Reading JW publications a few times a week) and "progress to baptism," and maybe that would make her happy. Would probably make you miserable though if you don't have any patience for cult mind control. But hey, if you think she's the only girl for you maybe it would be worth it.
The final option I would suggest (and the one I would personally take) is cutting the relationship off and finding a girl who won't try to put the religious dogma she gets from a publishing house in New York ahead of your happiness.