How to clean my full suspension bike
If  I want to get it "Concours d'elegance" clean, I use dish washing detergent. 

Unlike a car, a bicycle has no issue with stripping off the wax polish that protects the paint work (I don't know anyone that polishes their bike), and the dirt is mostly muddy organic materials that needs a mild soap/detergent. (Spots of oil from a over oiled chain or hub are dealt with using a concentrated dish wash liquid/water solution). 

Main thing to do is keep any contamination off the disk brakes, hence the need for plain cleaners. You can go to the bike shop and buy bike specific cleaners in small, bike wash sized bottles, but I prefer to buy a gallon of basic cleaner and spend the change on things that matter, like a good coffee :) 

Cleaning to me means removing the grindy stuff from around the moving bits and lubrication of the moving bits. Normally my only focus for "Shiny clean" is the shock and fork stanchions, after all, its a mountain bike -a bit of dirt gives you street cred and makes the bike legitimate...