The good news is, some natural remedies are genuinely more effective than chemicals, in this case!
I read about bedbugs when our family and the one across the street (8 kids, between us - all best friends) came down with lice, this summer. Lice and bedbugs are typically treated with similar or identical chemicals. Both have been on the rise in the US lately, due to overuse of those chemicals. The nice, gentle-sounding alternatives like tea tree or grapefruit oil, I found ineffective. But both bugs can be very effectively killed, by heat! There is good science to support this, if you research online. Like any other living thing, these bugs have a limited range of temperatures in which they can sustain life.
Wash everything you can put in a washing machine, in hot water, on the longest cycle and dry everything on high heat, in a dryer. Don't forget things like pillows, stuffed animals and curtains. Carefully quarantine disinfected items, so they are not exposed to bugs from unwashed items - even clothing the washer is wearing. A low-IQ person would need help with this, since one mistake can mess up the whole process.
A steam cleaner will kill bugs on carpet and upholstery that won't fit in a washing machine. I'm not talking about the steam cleaners you rent and put chemicals in. I rented one, during our lovely lice episode, and had trouble getting the soapy water that came out of the machine to be very hot. The steam cleaners you can buy (which may be marketed as wallpaper removers) use only water and get nice and hot. They cost ~$60 at places like Lowes or Home Depot. Perhaps you could buy one and let your friend use it (I get a lot of use out of mine, for various cleaning jobs around the house); or she could buy it and you could help her resell it on Craigslist after she clears up her problem. It's important to let the steam sit in one place for several minutes, not just sweep over it for a second or two, with the wand. It will get things like mattresses and cushions pretty wet - you'll need some fans, for thorough drying - but it's better than bugs!
Bugs on humans (more of an issue with lice, but it can still be an issue, with a serious bedbug infestation) can be killed by sitting in a hot sauna for 20 minutes. This is 100% effective! Can you get a trial membership at a Y and bring your friend and her family, as guests? Or, she may be eligible for a discount or free membership, based on low income. Obviously, hit the sauna before allowing any of them to sit down on furniture or do anything else that might spread the infestation to other members.
Bedbugs can also survive - temporarily - in clutter, like stacks of papers. Get rid of what you can. Put what you can in sealed, plastic bags for several weeks. The bugs can't survive indefinitely, if they never get access to a living food source. Expose what you can't store, to heat: clean everything possible with scalding hot water; if possible, turn up the heat in their home as high as you can and have them all leave the house for a day; or, if you're in a warm-weather area, you can drag things outside in the heat of the day and expose them to sunlight for as long as possible. It may be impossible to heat-treat every last thing in the house. But the fabrics that come into contact with human bodies are the key things to treat. If that is done meticulously, then cleaning other items as best you can should be enough.
Edited by VocalMinority - 2/17/12 at 7:29am