I flush but don't refill the bowl.
Give a good shot of liquid dish detergent in the bowl, then fill with water,wait a few seconds then flush the sudsy water down .
For stubborn stains or rings leave the soapy water in the bowl till the next use.
No fuss no muss or nasty brushes to stink or clean.
Good Luck, Mike
"wine is a constant proof that God loves us, and loves to see us happy" ben franklin