I don't quite have my ducks yet, so I can't speak to their specific needs, but I have had chickens for quite a while.
The main problem with having chickens on plain dirt was just that the poop got kinda stinky. The main purpose of bedding, as far as I can tell, to cut the smell and make things easy to clean up. (Bedding is often referred to as "carbon" against the poop's "nitrogen," AKA ammonia. This terminology comes from composting, where you need to have both to have an effective compost pile. You can tell you don't have enough carbon if the compost stinks.)
However, as a total cheapskate I hated to pay for bedding. After some experimentation (newspaper, tree mulch, etc.) I found out that I can get coffee grounds for free from Starbucks. My local starbucks fills a 5 gallon bucket full of coffee grounds every day. So I leave 2 buckets and pick them up every other day. The coffee grounds do a great job of keeping the smell down, then I can just shovel them into the compost bin. I get a fresh smelling coop, and top notch compost very quickly. I assume this will work at least as well for ducks and their watery poops.