I use a Hoover SteamVac on wall-to-wall carpet and it does an excellent job, but I'd expect Bissell to be similar.
I'm allergic and also bothered by chemicals, but never had a probem with Hoover's or Bissell's carpet shampoo.
Bissell has one shampooer that looks interesting.
"Big Green Machine Professional 8623" - Good Housekeeping Seal.
But, it looks much too heavy and bulky for me and I can get my rug clean without something like this.
Never had much luck with carpet cleaning companies including Stanley Steamer. Rug never looked clean so I tested it using a wet white cloth. Always, residue on the cloth was varying shades of light gray. Carpet isn't gray.
Decided to do it myself and found how clean and dry it gets depends on the effort to get it clean and dry. One or two quick passes won't do it. I know it's clean when the rinse water is clear and no more water is extracted from the rug. My carpet usually dries within an hour. I try to do it in the summer when the AC is running. AC's are also dehumidifiers. Afterwards, wear a mask to spray it with Scotchguard for rugs.
Also, it's easier to clean when you're using a good vacuum cleaner that removes deep down dirt.
It is time consuming and sometimes tedious, but there's satisfaction knowing my rug is clean...and funny thing, I actually enjoy doing it. Don't ask me why. I don't know.