How can I shake this feeling that I'm bugging my friend? A bit of a rollercoaster relationship?

Your friend might just be a little confused. Just be nice to her, try not to get in her face, and most of all listen. If she needs to talk to you about your situation, let her. She needs to speak her mind, and you need to speak yours. Tell her you still want to be friends with her. Ask her to go to a movie with you, or maybe the mall. I don't think your bothering her. She might just need some time alone.