If I was to use a 50/50 solution of water and bleach, would the fumes get rid of cockroaches? I have sprayed them with the same solution and it kills them dead. Of course I don't spray the solution on carpet.
Call an exterminator. They will rid your house of them.
A more safe approach it to go to your druggist and ask for boric acid. It will be a rather small bottle. Mix a teaspoon of the boric acid and a teaspoon of sugar and put it in a small jar lid and put it back under your stove or any place that is inaccessible to your beloved pets or small children. Roaches love it and it will eliminate them shortly. You can make as many of these as you need, and have safe places for. I have used this in the many places I have moved into where the roach population was gross and they were eliminated shortly.
Hope this helps.
Do remember to put in safe places.
I use spray polish like Pledge, only the cheaper off brand bottles to kill roaches on the counter. If there are a lot, go in and watch where they go and then vacuum any of them you find. If you see lots of them, vacuuming is the way to go. Then store the vacuum outside for a while or empty the contents outside then spray them pledge like furniture spray, the orange variety, or kill them with bug spray.
Roach motels are great, you need to keep checking when they are full on one side and then turn it over for the other sticky side. You will go through a lot of these...and throw them away. I spray them before I throw them away. Also, you can wad up bits of duct tape, sticky side out and catch them that way too. Cover up the sink at night, some of them come up from the drain.
I use bug spray cautiously, but when I find a nest of them I can use it away from food, etc. I use non stick spray to kill kitchen ants on contact.
Other simple ideas:
Make roach baits.
Mix together syrup and yeast granules to make a paste. Drop globs onto jar lids and place along counter tops against the wall or under cabinets. Mix equal parts baking powder and confectioner's sugar. Put this mixture out on small lids on counter tops and under cabinets for bait. It takes a while, at least a couple of months if you are not using an exterminator, and if it overwhelms you, then you would probably find it worth it paying for an exterminator.
I don't know if those little boogers would be resistant to that solution or not but you certainly aren't resistant :-( Bleach is horrible for your health, including the fumes your lungs breath in, and horrible for the environment in general. Try the boric acid or roach motels already mentioned and if they don't do the trick then it would be best to call an exterminator.
Alcohol won't kill cockroaches. They have been around for millions of years. They went hundreds of years frozen in ice. In scorching heat, and even have not ingested food for years and the buggers are still around, 'they will be back'.