I go for a ride in the rain and hope that it will wash the old muck off
I might have said differently either here or elsewhere but I'm pretty fluid in my cleaning regimes and I don't really get involved in it enough to remember if I'm following a regime or not. All my bikes have full mudguards and flaps. They tend to get cleaned before I have to do any other work on them or when they're starting to embarrass me. My bikes get ridden in all weather conditions.
Sometimes I will give the drivetrain a proper go-over, even taking the chain off, but usually it's a spray of the chain with WD40 or GT85, followed by a rag down then some lube then some more rag-downs. Whilst I'm at it, I might wipe the frame down with one of the rags. For a "better" clean, I will spray with Muck-Off that I have been given, followed by a brush assisted hose down, dried off and wiped with an oily rag (it helps keep the dirt from sticking imho). Lubing is done as required. When the Muck-Off runs out, I plan on replacing it with car shampoo. I use a common old garden hose and not a pressure hose.
Rim-braked bikes are bad for getting mucky but the Brompton is the worst - it never stays clean for long and often needs the chain going over just to stop it going orange and squeaking, especially in the winter. My newest bike is the best in this respect - disc brakes, Rohloff hub and a belt drive - it doesn't really get that mucky and usually a hose-down is all that's required.