Hello eleanor-rigby. I'm also 20 and dealing with bipolar II.

If it's any comfort to you, you're doing better than I am- I've never even been in a relationship! Haha. What you're describing could be a symptom of borderline personality disorder (which can look very similar to rapid-cycling bipolar II). People with borderline tend to have an intense fear of being abandoned. It also could simply be a personal quirk. It is not, as far as I am aware, something that is related to bipolar. Regardless of where it comes from, it probably is best addressed in therapy.
Hope that all that helps. By the way, I love your user name. That is probably one of my favorite Beatles songs...because I can really relate to it.