I had a similar problem with my Dixie when she was a pup. Her problem wasn't necessarily pooping in the crate though, it was pooping in the house. She would poop in her crate though if she had to go.

I solved this problem by putting her on a very regular food schedule and making sure she pooped before letting her back in the house. If I let her outside on her own, she would never go. I actually had to train her to "go potty" on command. Then I determined what time of day she reguarly went. For her it was in the morning. Basically, I knew not to leave for work until she did her morning poop or I would come home to a pile to clean up. So I went out with her and gave her the command "go potty". If she only went pee then I would make her go back until she did a poop. Once she realized we were not going to play or go back in the house in the morning until she did this, we didn't have any more problems. A friend of mine had the exact same scenario except hers was at night. Going out with her pup and making sure she went was her solution.

Of course you never want to crate a dog for excessive amounts of time. Once a dog is house trained, I never crate them at night. I may close the bedroom door so they don't have access to the rest of the house but I do let them sleep in the room. It doesn't matter if they don't sleep in bed with you. I still think they want to be in the same room. Perhaps you could put a comfy set of pillows at the foot of the bed on the floor and encourage her to sleep there.