ETA: If you are pregnant, have someone else handle the DE. You can "deactivate" it with water, but you still don't want to breathe it much.
You have to treat for fleas every couple of weeks to get the newly hatched fleas. Something that works but is a mess to deal with is diatomaceous earth. You can spread it on the carpets and let it sit. You want food grade. Then you want to use a good vacuum or shop vac to get it up (wear a mask) again later. We did this to all our carpets when we were gone for a week. We also got a better vacuum and vacuumed our carpets a lot - and vacuumed the beds, under the beds, the couches....we washed all the area rugs (like the bathroom rug) or got rid of them, bagged or washed toys, treated the cats with a long-term application (in our case, Frontline Plus)...if you are not treating the cat with a good product, then the poor cat is a vector.
In our case, the poor cats got fleas from us - they never go out, so it had to be that we brought them in.
I grew up bombing the house, but part of the issue with flea bombs is that they coat everything and then you end up having to re-clean the chemicals everywhere. And that they can become superbugs. Not that DE isn't it's own cleaning issue but I'd rather have something that will be negated by water than be worried about the chemicals. You should treat the cat with something like Advantage or Frontline (and get the vet to show you where on the shoulders to apply it) and vacuum, vacuum, vacuum - everything. And wash all the bedding, any clothes that have been out, etc. Get out that crevice tool for your vacuum and get all the nooks and crannies and dump the bag immediately outside. Do this once a week or at the very least, every two weeks for a while.
Fleas are something that exterminators will treat for but as long as you have a pet, they WILL NOT guarantee their work. So we decided to skip the $$ treatment because our fleas weren't that bad yet.
If you actually have bedbugs, that's a different problem.
http://www.orkin.com/other/bed-bugs/