Girl problem! Help! Please read! ?

Ok so I've known the girl in question for exactly a year, and in the year we have become so close we are almost boyfriend and girlfriend, we kissed, we've had sex, everything, but still she tells me that she doesn't want to be in a relationship with me :/

We love each other, but I think she is scared of what other people will think, because there is a 3 year age gap. She always says that "we are just a bit of fun", but I spend almost every night at her house, and we usually end up doing something sexual. However, a lot of times she has told me she wants to stop what we're doing, because it's not right. I agreed to it everytime because I respect what she wants, but then no more than 5 meetings after she said this we can't help ourselves and it happens again. Now, I really really love this girl, and I am on holiday with my family in the US right now, and she is on holiday in Turkey with her friend and friend's family. Before the holiday, we'd started to drift a bit, and argue a bit, and I was convinced that we needed a break for a bit, hence the holiday. Now I'm away I miss her intensely, I'm almost depressed without her, and I'm worried she's going to have a fling on holiday or something. I've contemplated asking her to be my girlfriend a lot of times, but never actually doe it. Does anybody think I should when we're both back home? I was thinking of buying her a new charm for the Pandora bracelet I bought her for her birthday, and a small bottle of the perfume she likes, then taking her to the park and asking her there. Is this a good idea? Am I risking what we have, or should I go for it? The fact she's wanted to stop what we're doing a couple times, could that mean she wants me to ask her out so we're doing things in a relationship kinda thing?

Basically the question is should I ask her out?!

Thanks people, sorry it's long!