I'm going to follow this to see what others say.
My son wanted to give our beardie a bed. We were at the pet store and they had a small dog bed on sale for $4 so I figured at that price we could try it. We have it set up on it's side so it leans against the two back walls at an angle. It sits right under his hammock and he loves to lay across the top of it. When we first put it in, he was actually crawling into the bottom of it at night for sleeping. Then he figured out he could get on the top of it and the curling up in the bottom stopped. It's a pretty fluffy bed and he hasn't had any problems with his nails getting caught or anything like that. It's not an ergonomic bed, but this is the closest thing to what we have that I could find.
As long as the bed is safe, there isn't any reason they wouldn't be allowed to have it - they may or may not use it though. Avoid anything ingestable, with dangerous materials, sharp edges etc. Some folks will wrap their dragon up in a fleece blanket or in some other blanket/snuggle sack. A few folks have dolls beds etc too, and tuck the dragon in after lights out. Blankets might get pooped on, so washable or disposable is a plus.
I like a natural look, so I just give hides. I used to have little fleece nests (just a pile of scraps) but it never got used.