Agree with Josh. Use three buckets. I do the same thing, only because you don't want any leftover brake dust and grime mixing in with any soap you apply to the paint. Also, wash your wheels/tires/wheel wells before you work on the body. This way, water doesn't dry up on the paint as your scrubbing away at the wheels. If you haven't used Sonax Full Effect wheel cleaner, give that a try and you'll swear by it. A bit expensive, but works great at areas you can't reach easily. Especially effective if your wheels are super dirty. I use it every two to three washes and just use less expensive wheel cleaners in between.
On drying, stay away from terry towels. They will put swirls on cars with better paint than ours, so try this instead.
Drying Towels
or
Adam's Great white drying towel
You can also use and electric leaf blower or MetroVac. No rubbing=no swirls