How do I find a home for my skittish cat?

I have a female cat who was the runt of a litter who I took in and brought back to health. She is 1/3 the size of a normal cat, and is a little over a year old now. Shes not fixed and has no shots. I cant keep her anymore because im living with my dad and he wants me to get rid of her. She is skittish and timid, but loves the people she knows. She has a slight nipping problem, when you pet her and she likes it she gives you love bites. Never hisses and is mean, she is a sweetie. I tried finding her a home, and the lady took her after me trying to catch her for like a half hour (scared of new people) and she brought her back a couple hours later because she peed on her, and was scratching her because she was scared, not scratching her being mean, just trying to get out of her hands. I really dont want to take her to the shelter (nonkill always) because its sad her going from sleeping on a bed to a medal cage. I dont think she would ever warm up to anyone in a shelter and im scared she wont ever get adopted :( What should I do? I live in Palmdale, California. Im completeley lost, and im willing to travel up to an hour away to find a good place for her. Suggestions?