Search Results: giving him another chance

This is a long story that I will try and keep very short. I met a girl last summer through a family friend. We met up for lunch and messaged a lot but she avoided hanging out. She then went to college andf throughout the year I kept in touch by text messenger and snail mail. At first she told me she was seeing someone but then said "If you want more than friends thats never going to happen and thats not a dig at you its cos im Asexual im just not programmed that way. she describes herslf as an aromantic lithsexual. I then admitted that im a virgin who's never had a girlfriend.
She became a bit more chatty after that and we hung out for lunch when she was back from college (I Paid) it lasted about an hour and a half and she gave me a hug at the end.
About a month after that I suggested going to a museum about 20 miles out of town I picked her up from her house and drove there and back it lasted about 4 hours all in and then she invited me in for coffee and something to eat and it lasted another hour or so but she insisted on giving me half the cost of the day out.
About two weeks after that I suggested we drive out to a castle about 60 miles out of town and again I picked her up we drove there and back (it lasted about 7 hours but she insisted on paying for half of everything mostly. We drove back and she asked me in for coffee but I had work so I declined.
She invited me to the pub where she works to see her and give her a book I'd bought for her but it was very busy and we didn't get much chance to chat (She text and thanked me for the book which she said was fantastic and apologised for not having much chance to talk).
How does it sound like she feels towards me and we see each other for the last time until possible late October next week what should we do? I get a buzz spending time with her and want to see her more and more but its not a sexual think i dont think spending time with her just makes me smile. Should I tell her this or not?