I just noticed this before, it is probably just coincidence and nothing else.

Whenever my character sits on a long bench and serana is in range, she will immediatley sit right next to him. she doesn't idle at all, she just does it as soon as he sits down.

Has anybody else noticed this or is it just me?

She obviously wants your character, that is the only reasonable explanation.

She interacts with other things if she is left idle for a while. If she is left idle near a cooking pot, she will began cooking. If left near a chair, she will sit down.