Well it seems like she's the one asking you out. You've already gone to the beach with her, and her house, on her recommendation, correct? Most people struggle to get to the point where girls will, say, go to the beach with them or allow them over. I think now all you gotta do on your end is find out said girl's feelings about you, whether or not they're platonic, or if she's romantically interested in you. But as far as "asking her out" you're already spending seemingly plenty of time together, so you asking her out could be a redundancy at best, and awkward at most. At this point, if you continue spending time with each other, you have to find out your feelings for each other. I think as far as that goes, instead of putting yourself on the spot and pouring your heart out or whatever, just ask how she feels about you, and then I guess if she asks you after, you tell her.
That's my assessment, anyway. I've never had a girlfriend ever, though, so my advice could be entirely ret*d.