The long answer is somewhat involved. Bush says it varies from gun to gun. Some like to be squeaky-clean, some shoot best when they are slightly fouled, and others need to be filthy dirty to perform at their best. Says Bush: “At still target shoots, most shooters are very aware of how many shots they've fired between cleanings. Some will clean after every shot and some after every third or fourth shot. Doris has a gun that gets better and better until the twelfth shot, then the patterns fall apart. The ammo used can also influence when you clean the bore. It's really all about knowing your gun.”
The only way to find out what your shotgun likes best is to start by deep cleaning it, according to Bush. You get a brush soaking wet with Hoppe’s #9, scrub hard for four or five minutes, let the barrel sit, wet, for ten or fifteen minutes, then scrub some more, then run patches through until one comes out clean.