She clearly wants to spend time with him. It's clearly important to her. But he's making the effort to push closer, and she's getting too self-conscious.
Also, funny thing, looking up about 'pain in the ass girlfriend', I stumbled across some stuff saying you want someone like that because they challenge you. And, to be honest, she really is basically challenging him, whether she realizes it or not, to do better, to be better. If he really is serious about her, he's going to have to push boundaries and bridge those gaps.