Note: Spraying the matresses with DDT is guaranteed to eliminate bed bugs. Ain’t progress wonderful. 40 years ago there would have been no problem.
DDT wiped out the bed bugs 50-60 years ago. However they are now allegedly resistant to it. The missing weapon accounting for their resurgence supposedly isn’t DDT (banned by Nixon), but a couple of other pesticides banned by Clinton’s EPA in the 90s.
Not that simple, but many things that could work are illegal: http://www.conservapedia.com/Bedbugs