My wife and I experienced 35 days of rain on one tour. Keeping bike clothing dry was an issue. We use Ortlieb panniers so the rest of our gear was dry. I've taken only 2 pairs of shorts for tours up to 3 months long. I'm not sure how may bike shorts my wife takes, but I think she also takes only 2 pair.
Something that you might try that works for us is to use a camp towel to help dry your shorts. Rinse your shorts or hand wash them in sink. After the rinse hand wring them to remove as much water as you can. Lay your shorts out flat on your dry towel, and roll up the towel and shorts. Then laying the roll on the floor, step on your towel (barefoot) several times. Hang them inside your tent, or if they are not quite dry by the time you are ready to sleep; and you have a synthetic sleeping bag, you can put them in the foot of the bag. They may be a little damp in the morning but they are wearable. This technique also works well in motels, using motel towels. Then get creative and string a clothesline, and hang them.
If you are in an area where a laundromat is available put you bike clothes in a dryer. We don't usually use a clothes dryer at home for our bike clothes, but on tour we use them when they are available.
This method used to work well in motels, but since most of them have switched to LEDs it is not usually an option.
They dry better this way than laying the flat. Wet clothes can also be hung on hangers.
There were 4 of us on this trip.
