Hi N.,
Same issue here. I did quite a bit of research because bug bombs make me very nervous, especially around small children. I don't want them playing in a home that has a fine coating of pesticide all over everything, you know? What I found in my research was that you can use something called Diatomaceous Earth. It is a fine white powder (it's not a chemical, it is actually tiny, tiny fossilized remains of microscopic algae from millions of years ago - who knew?). The way it works is that the flea comes into contact with it and it makes a scratch in the flea's waxy coating. The flea quickly dehydrates due to this scratch, and dies. It is not toxic but is quite effective, according to the many websites I found on the subject.
Meanwhile, use Frontline on your cat every month. It protects against fleas and ticks for about a month and is not harmful to your pet. It is expensive to buy from the vet's office, however you can buy kits on eBay and other places where you get the "big dog" version of Frontline, and decant that into a glass vial. They give you an eyedropper thing and you just squirt .5ml onto your cat each month. It's only about $1.75 per month that way, vs. $15 if you buy from the vet's office.
You can also use the Diatomaceous Earth outdoors, however it does wash off with water (or vacuum up, indoors) so that is something to be aware of. Good luck! We are treating our house, yard and cats this weekend to get rid of the nasty little fleas that are everywhere! 'Tis the season...