New cat won't use litter box?

We just adopted a 5 month old female tortie-tabby mix from our local humane society. She had a clean bill of health and had been eating and using the bathroom regularly there. She is currently quarantined to a room by herself with food, water, some toys, and a just washed litter box with fresh litter in it. Her litterbox is nowhere near her food. However, she has both peed and pooped on the bed but not in the litter box. I know she's stressed, but is this from stress or a possible health issue?

Also, she is not our first cat; we're mostly worried because we've never had a cat do this, but we've also never had a cat get this stressed after bringing them home.

L2014-09-01T14:32:24Z

My second kitten did this, I was so shocked because I had previously thought it was instinctual for cats to gravitate towards a gravelly/moveable material to pee and poop in! He did it on the bed, the sofa, my partners back in the middle of the night!! Ha.
I decided perhaps it was the man made litter he found odd and so I put fine soil in the tray. He began to use it then I suppose because it was a natural substance? I then slowly mixed litter in with it each time I changed it and eventually it was back to being just litter again and he's been fine ever since!

?2014-09-01T14:30:29Z

Give her time to acclimate. If it's a 'covered' litter box, take the top off. It could be that she doesn't like the litter you are using. Just give her a little time. Probably a little skittish.