Holyyyyy crap awkward. He's really respecting and liking Selina a lot -- and really grateful that she's been so helpful, although he's increasingly becoming suspicious as to her motivations to her funding. If only because Batman's paranoia has somewhat become contagious, hence suspicions. OTHERWISE, he does really care about her and considers her a good friend. Would totally date her, but knows he's not exactly her flavor, so to speak.