Honestly, I would probably be the one ignoring the girl and not on purpose, mind you. It's just my nature *shrug* I never initiate conversations and only speak as much as needed, meaing I don't go into details unless forced, I keep my emotions to myself - whatever they may be, good or bad - and I'm generally too occupied with myself to be bothered with the partner. Of course, why would she go out with me (Never been in a relationship) if she didn't know this already? O.o
As for being ignored, I honestly doubt that I would notice such a thing. I know I'd be far more than irritated though if she wanted to spend every waknig moment with me, that would be the problem and not vice-versa.