I usually won't *begin* a training ride if it is raining, but once the bike is wet and dirty, you gotta wash it one time no matter how far you ride, so you might as well make it worth while.
I have quick links, so I'll take off the chain and wheels and put it on the stand in the front yard. Then a light fresh water rinse, some diluted car washing soap and wash it down. Follow with a light rinse. Just don't blast water into bearing and parts.
After that, I'll wash the wheels and then wipe it all down. I usually soak the chain in some mineral spirits, then lube it and put it back on. Pivot points all get a shot of tri-flo. Saddle gets some leather conditioner.
If your BB doesn't drain well, pull the seat post for a day or two to let it air out.