Worm composting is a lot like ordinary composting in that it's important to mix together the right ratio of browns (high carbon materials) and greens (high nitrogen materials) for efficient composting without a bad smell.  In the past, greens have been in short supply on our farm, but now that we're getting food scraps from a local school, we're suddenly short of browns.  The browns make up the bedding in the worm bin, covering up the food scraps so that they don't smell and keeping the bin damp and aerated, so we really can't skimp there.  Time to do a bit of research and figure out which waste materials can be used as bedding in a worm bin:

• Shredded paper seems to be one of the best options, as long as you steer clear of glossy magazines and seed catalogs.  Once separated into small strips in a shredder, paper soaks up water well, and the spaghetti-like strands tend to stay fluffy, allowing lots of air to get to the worms.  We had planned to focus on shredded paper for our worms' browns, but quickly ran through our junk mail and needed much more!
  
• Cardboard is another good option, although you have to tear corrugated cardboard by hand.  (The thin cardboard that many foods come in goes through our shredder.)  Several people have reported good luck using cardboard in their worm bins, but it's essential to keep an eye on it and make sure the cardboard doesn't mat down and make the bin anaerobic.
• Autumn leaves don't require any work to prepare them for use in the bin, but can tend to mat down.  Also, they don't absorb as much water as other bedding materials, so you risk having your worm bin dry out.  It sounds like leaves make a good bedding when mixed with other high carbon materials, but probably aren't the best idea by themselves.
• Cardboard egg cartons were suggested to me by J and I think they have a lot of potential.  They're easy to rip apart, and I suspect that the complicated shape will make them much less likely to mat down than traditional cardboard.
• I've read about people using other materials for worm bedding like straw, coconut coir, and peat moss, but those would all have to come from the store for me, so they fail the "waste materials" test.
  

Since I was itching to put the first round of food scraps in our bin, I went ahead and gave all of the free options above a try.  I (mostly) segregated the bedding into zones within the bin, so I should be able to tell which ones work best for us when I come back through in a few weeks to check on the state of decomposition.