What a beautiful kitty she is!
Sarah and Mandy and Ellie have given you great advice. The thing that will probably bring her around the quickest is for you to not force things. I just wanted to add a couple of things. In addition to a tall cat tree, you could give her a couple of other "safe" spots with comfy beds or blankets. She might like a cave-type bed or one with tall sides, so that she can hide in them. Put them in out-of-the-way places where it's quiet and there's not much traffic, like a closet, or even under your bed, since she already seems to feel safe there. She'll view prolonged eye contact as aggressive behavior, so when you sit with her, don't look directly at her and don't try to pet her (hard as that will be - her fur is just inviting snuggling!) at first. Let her sniff your hand and give you the ok before you touch her.
Was Baby this fearful with your friend? She may just be a timid cat by nature, in which case it will take her longer to feel safe around you. I have an extremely skittish cat who I adopted when she was 1.5 years old. She's been with me for 13 years now. Any loud noise, or loud person (including me), will send her under the loveseat. If I raise my voice on the phone, she disappears under the loveseat. I'm a small person, but if I walk towards her too fast or too heavily, she freezes then runs away a few steps. She'll stop, turn around to see if I'm still coming towards her, and if I am, will just keep running. I always have to move very slowly and very quietly around her. Did I mention that she's lived with me for 13 years??
Though it might take some time and patience, once Baby trusts you, you'll likely have a velcro kitty. There is something really rewarding about being one of the very few people a fearful cat has deemed worthy of her trust.
The three people my 8-lb. cat allows to rub her tummy were so proud the first time it happened that it was kind of hilarious.
She's going to love living with you - she just doesn't know it yet!