You could certainly frame it in the context of asking for a collaborative project, but I think it might come across better if you propose a project that you would be interested in undertaking, and asking if that would be a possibility under her mentorship. This way, you would come in with an understanding that there are opportunities to do the kind of research you are interested in, and she would not be surprised concerning your focus. You say that you're interested in connecting to the bigger pictures implications, so propose something that would demonstrate that! Congrats on the acceptance, too