Asking out a girl who thinks I'm a dick...

I put on a bit of an act to some girl friends of mine, knowing that they think it's hilarious how cocky and enigmatic I am, though I'm pretty confident they know it's tongue in cheek and I'm secretly very genuine and down-to-earth. I didn't anticipate developing feelings for one of them. I'm pretty confident she feels the same about me - crazy eye contact, making effort to be around me and directly engaging me in conversation in groups more than others - but am worried she might be apprehensive about letting herself fall too deep emotionally because of my persona.

I'm confident that once we're alone and able to chat I can show I have a deeper side than the playful act, but feel that I may need to get a little spark of it in before I could arrange a date with her.

Does anyone have any suggestions? Do I open up (possibly a bit weird/sappy/fake sounding); try to show it through behaviour (people will probably notice I'm behaving out of character); or just go for it and ask her out straight up next time I see her (my nerves will probably expose me a little)?

I should probably have added that I think she hated me at first. We've known each other for over a year now. It could well be that she's heard different things about me that have changed her perception. I think to be the same guy is not an option - it's not something I want to be with anyone I'm really close with and all my closest friends know I'm very thoughtful and caring.