Do they really need bedding?

unless you are a deep method person than a thin layer would be good.  You want something to absorb the wet.  Maybe half the amount but there should be a little something down.

If you don't use any bedding you chickens feet (and so your nesting boxes) will be covered with poop.

Shredded paper, leaf mulch and lawn clippings are free, you can offset some of the cost of pine shavings by using free bedding most of the year. 

I do not used deep bedding. I do use recycled paper pellets called "Crown Animal Bedding". It comes in 40 pound bags, one of our local feed stores sells it for $9.00 a bag the other for $20.00 (seriously!)  It's 100% recycled, low dust and very absorbent. We keep it about 2" deep. It's easy to pick the poop clumps out, especially since  I make my kids do it. They do it twice a day with a kitty litter scooper and dump the whole mess right into the compost pile. I add more pellets it as needed. We don't have a walk-in coop so it's not an issue here but unfortunately the bedding pellets do tend to  'travel' so you might have to but a 2x4 in your doorway to keep them in the coop.

you may check and see if you have a local saw mill in your area. I can go get a black trash bag full of shavings for less than 1.50.
 

I had to do a lot of foot washing while the checks were in the small brooder. so 'poop foo't, or rather avoiding 'poop foot', was one of the determining factor in deciding coop size.