I wonder if freezing would work as well for cotton fabrics as it does for the various insects that like protein fibres?
I'm a handspinner and learned to seal all fleece that comes into the house into the appropriately sized ziploc as soon as it comes into the house. It goes into the freezer for a week or until my husband says "Honey, is it time to take this wool out of here?" Then I take it out of the plastic and it joins the rest of my stash of spinning fibres.
Well, a quick google seems to indicate that three days at minus 26 degrees F (26 below zero) will kill bedbugs. If you really don't want to prewash, this might be an alternative.