pk-bailey, I'd just like to comment on what you said about how you can only pick her up once she's just woken up. The majority of cats don't like being picked up. They can either not respond, squirm, hiss, wriggle out of your arms, and it can make them tetchy and a bit timid, and aftewards they may go and hide.
I would suggest avoid picking her up at all, especially after she's just woken up, as this is when she's most vunerable. I'm guessing even when she's completely relaxed and affectionate, she just won't like being picked up, and by doing this you're making her wary of being touched.
Just sit in the same room as her, reading a book or something, and she may come over and sniff. If she does, don't immediately go to pet her, just let her sniff you, and talk to her in a high-pitched, soothing voice. We've had Minsky for 4 1/2 months now, and he is quite affectionate, but still if he comes up to sniff at me first, rather than me going over to him, if I go to pat him on the head he'll duck down and run away.
I've read that in cat-dynamics, the 'dominant' cat is the one that walks over and initates contact. Unlike dogs, the way to show a cat your interested is to maybe avoid eye contact, act shy and demure yourself, and slowly build trust.
Cats are funny creatures, and can have 'off' days, although I appreciate that Bailey hasn't been 'on' really since you got her. I'd give her more time and give her space. It sounds strange, but less physical contact may make her more trusting. I find talking to them whenever they're around in a high-ish voice helps
Good luck!