“This is precisely the area that the researchers, from Imperial College in the UK, targeted with their gene drive system. Males that carry one or two copies of the edited version of the doublesex gene develop perfectly normally and are fertile. Females with only one copy also develop normally. In all these cases, these animals will experience gene editing, and all their offspring will end up receiving a copy of the edited version of the gene from them. And females where both copies have been edited develop with a mix of male and female traits and can't reproduce.”
So the majority of offspring carrying the trait can reproduce. The gene drive mechanism ensures that while the change reduces fitness, it still spreads through the population.
It does this, because even if the gene drive modification only exists on one chromosome, it will copy itself to the other chromosome.
If we were to try to eradicate them I think using multiple techniques at once on a global scale would probably be necessary. You want to get them ALL. There will always be that one place with a bedbug population in isolation waiting to reintroduce them to the world.
Now that I think about it. This would make a great startup idea.