last year i drove my G in the winter so i put her up on ramps in the Spring and just cleaned her off with a large water bottle, car shampoo, and wheel brush while i did the oil change.
if you have a lawn sprinkler, you can place that under the car and let it run for 30min given that you can get your car high enough off the ground. that's one of the easiest ways to wash under there per another car enthusiast from the MINI forum.