DE works well against larval fleas because they thrive on a high humidity environment and cannot travel very far or move very fast. Larval fleas look like little transparent worms... DE could effectively break the cycle of fleas in the carpet by dessicating eggs and preventing larvae from pupating into adults.
However, bedbugs can climb on walls, headboards, luggage, dressers, mattress seams, folds in your sheets... they're perfectly capable of walking or climbing on anything that isn't slick... so they could get away from an application of DE/dust in the carpet. Bedbugs also don't have a larval stage. They hatch as nymphs (just smaller versions of the adult) and probably wouldn't be as susceptible as an arthropod that has a larval stage would.
I still want to test this in the lab though and see how it would work in a laboratory situation with constant exposure. There are a lot of products that claim to work against bed bugs and aren't regulated by the EPA but when we test them in the lab, they don't hold up to those claims...