Using mild soap not be a problem, only things like muck off are a problem because they are very strong, but still wont dmaamge the bike really. The only tinhg oyu need to be worried about is getting water in to the bearings, so dont use a hose near any bearings!
Asuming you dont have a bear steel frame you dont need to dry your bike after cycling in the rain, but what you must always make sure to do is grease the drive terain with somthing such as GT85. this is the most vital part, my bike looks like its never cleaned, because i very rearly do, but thats not important, the important part id that you look after the driver terrain and other 'moving/working parts' as i call them.
That includes putting a solid greese on to the skewers so that it gets in to the hub bearings to keep it in good working order. Your main priority is the driver train also look after the brakes thou. Keep the drive terina clean not only to sotp rusting but to stop corrosion and lower resistance. The dirt acts like sand paper!