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.