Hey, Barb: I don't think it is necessary to cover a raised bed. Treat it just like the dirt in your yard. If you are trying to save some plants over the winter and are in a cold area, covering might be helpful.
Yes, you can use leaves or other biodegradable paper or bags to Cover it.
Do you mean as in a canopy or a bed skirt? Personally when I do a raised bed for a client, I do add a bedskirt, so there can be underbed storage. I have found over time, I don't like canopies as they are massive dust collectors unless your going to take them down monthly as wash - too much work for me. Now mosquito net canopy is another matter as that will keep me from getting eaten alive during spring.
LOL guess I didn't get it was a garden bed. I do cover garden beds for my winter crops using hoops and plastic.