Question: Three weeks ago, I adopted a 9-month-old female cat, Kira. On the ride home and for a little while after, she seemed pretty calm, though withdrawn. She's set up camp in my bedroom and has food/water/litterbox there. When I'm awake in the room, she stays under my bed almost exclusively. Sometimes my roommate can coax her out, but I never seem to be able to. Typically, I'd go under the bed to retrieve her, which I've now learned is the very wrong thing to do. Now she's terrified of me, and sprints away whenever I approach her, desperately searching for a place to hide from me. She still doesn't do this to my roommate. Did I screw this up beyond hope of repair?

Answer: 
There could be more going on that might deteriorate your relationship with your cat. Looking directly in their eyes for example means a threat in cat language. Moving directly towards her **and** looking her in the eyes is the equivalent of an attack.

Repairing the damage might take some time. Start by offering good smelling, tasty treats in a passive way. 

* Move calmly into the room
* Sit down on the floor. Lean sideways and prop yourself up on one ellbow if you can hold the position for some time. This broadcasts relaxation.
* Place a treat at arms length beside you
* Close your eyes to narrow slits, do the lazy cat blink occasionally.
* Completely ignore your cat until she (hopefully) ate the treat and went away.

If this first step was successfull, you can step it up by placing the treat in front of you, then closer, until you hold it in your hand or place it on your lap.

Don't forget to not look directly in her eyes, but close your eyes a little and blink slowly instead. That way you tell your cat "I'm calm and relaxed, don't be afraid".
I had a similar experience with my cat, fortunately it lasted only a day. So not sure if this will help, he is usually under the sofa.

When you are calling their name, tap the couch with fingers or hand rhythmically. “Come
here baby 1...2...1..2” they will become focused on your finger movment and come towards you. My cats take it as a signal to play or to come to me. At this point I’ll excitedly say “good boy”, “good job” and spout nonsense about how much I love him in a coaxing tone . He digs that.

* I softly call his name and speak to him , while waving a feathered toy (distracting him with a toy helps).
* Treats, leave treats out near where the kitty hides (scatter them if you want), just make sure to ignore your cat when he sniffs about. Don’t be in a hurry to hold him.
* Make sure you are the one feeding the cat, cats are often more open to individuals who feed them.
* Don’t be aggressive in words or actions and I dont mean with the intention to do harm, but in terms of raising your voice, getting frustrated or hitting the surfacing to harshly to get their attention.