The unfortunate truth of riding your bicycle is that you will inevitably make your clothing absolutely filthy. I'm talking smelly, sticky, salty, doesn't-go-away foulness here. It's horrible.
On the flipside, it's not hard to keep your shiny new bicycle clothing looking shiny and new! Here are the two ways I wash my own clothing.
Prerequisite: find a color-free and fragrance-free laundry detergent. The fewer chemicals, the better. Avoid fabric softener. Remember that the job of proper laundry soap is to wet and emulsify stains, NOT to "look pretty" or "smell nice"! I keep my laundry soap in an old bicycle water bottle, just for fun.
Option 1: Sink Wash.
After every ride, I go into the bathroom, stop the sink, start running warm-ish water, and squirt about 1-2 tablespoons of detergent into the water. Then, I drop in the spandex I used on the ride: jersey, tights, socks, gloves. I wash these by hand, rinse 2-3 times or until the water runs clean, squeeze (not wring!), and hang to dry. In 40% humidity, it takes about 8 hours for everything to dry.
Option 2: Machine Wash.
Bicycle spandex is machine washable. Wash in cold water, and tumble dry on low or no heat. Drip dry if possible.
A stock of clean clothing is a right, not a privilege. Eddy Merckx made it a point of always having a clean set of clothing handy at races. There is no need to ride in unwashed, foul smelling spandex if you can avoid it.