How effective is a bomb to get rid of bed bugs?

Not very. Using a store-bought "bomb" will not get very well into the wall voids and equipment where roaches like to hide. If you're going to try it on your own, the bait works best but be sure to read the directions and put it out like it says. If you put out too big of a glob they might not eat it. If the problem is particularly bad, you're better off in the long run to hire a pest company to come out and take care of it for you; you might pay more at the start, but, for bad problems, you would spend twice that and will probably call them in addition.