I bought this big soft house brush at the hardware store the other day - off the dollar table.
It worked great for washing the nooks and crannies around the rear, and the rims and spokes, front disc, etc.
Soft! so it doesn't disturb ABS stuff, etc.
The back of us both were filthy when I got home. Clear up on top of the rear case was very dirty water. The back of my hi viz rain jacket and my helmet had muddy water on them.
The worst mess I've ever seen after a ride* - that is how dirty the dry roads were - then the rain came!
A clean scooter is a happy scooter!
I usually just let 'em drip dry.
Stig
*riders in the UK say they have trouble keeping their scooters clean - must be like my ride yesterday