I feel like my cat doesn't like me?

So I adopted a stray cat from the shelter about 6 months ago and she is really the sweetest kitty ever (she's two years old). However, she HATES to be petted and will bite pretty hard any time I try. She also loves to sit by herself looking out the window, but I hate to leave her alone. The only time she lays by me is during the night. She snuggles up tight to me all night, so I know she doesn't hate me but I hate that I can't be with her when I'm home. I feel like I'm abandoning her or something even though I know she is in a loving home. Advice please?