I have been doing a lot of research about natural solutions to managing fleas in the home and on your kitty. I do not like to use flea bombs. They are just to toxic for cats and humans.
If your cat will let you bathe him or her, I hear a very successful remedy is washing your cat with dish washing liquid. This was repeated over and over as a good solution. The soapy suds kill the fleas. You want to let he suds stay on your pet for a while so the suds can kill the fleas. I have read that the flea eggs will still be alive and they need to be combed out with a flea comb. My cats do not like to get wet so this will not work at our house.
Flea combs. If your cat will let you comb them, have use a flea comb and have a soapy water solution nearby to dip the comb in. The fleas will die in the soapy water. It was suggested by our friends, Dushi and Paddy's Mom at Cats in Trees that if you wait for your cat to be sleepy, they are sometimes easier with letting you groom them.
Two ideas that have been suggested are salt and baking powder. The baking soda kills the live fleas and the salt kills the flea eggs by dehydration. You can sprinkle one or both on your carpeting. Leave them on for as long as possible, 12 hours or more. then vacuum up. You can also powder your cat with the baking soda. Be careful not to get the powder in their eyes because it will burn.
Citrus oils. Cut a lemon in half, leaving the peel on, and soak in 12 oz. of water overnight. Put it in a spray bottle and you can spray your rugs, not soak them, and let them dry. Fleas do not like citrus. The lemon will kill the fleas on contact and repel them. You can also spray your cat with the solution but it is recommended that you add more water to dilute it. If your cat has any open wounds from scratching themselves, this is not a good idea because the lemon water will sting at the location of the wound. Also make sure you do not get the lemon water in your cats eyes.
Brewers or nutritional yeast, added to your cats wet food is both good for the cats health and a flea deterrent. I use about 1/8 a teaspoon per 1/6-1/4 can of food. they don't seem to mind the taste.
The last tip I have read about is apple cider vinegar. I put 2 drops in their drinking water every time I freshen their water. Their water bowl holds about 5 cups of water. After they get used to the taste, you can slowly increase the vinegar amount to 1/2-1 teaspoon every time you change the water. You can also make a diluted solution of the vinegar with water and spray or rub it on your cat. Fleas do not like the acidic nature of vinegar.
So I am trying all of these methods to see what will work best in our home. So far the salt in the rug worked well. I also powdered my cats with the baking soda. They did not like it but they had some relief from scratching for a few days. All of these methods may need to be repeated a few times until the fleas are controlled.