Contrary to popular opinion, bicycles are outdoor equipment, intended to be used out in the environment. They don't mind getting a little environment on them.
Except perhaps the saddle, depending. In rainy weather I carry a couple of plastic grocery bags and a couple of rubber bands. Stores completely in a pocket. Some people use plastic showercaps. That's all you really need.
If you don't believe me about the environment, here I am arriving at work one day on my everyday commuter.
And parked one day while out shopping.
Nine winters of environment, and it's none the worse for wear. A little water won't hurt yours.
EDIT: If you're worried about rain washing the lube off your chain, then you're using the wrong lube.
Lube made for the dry, or those where the selling point is that they keep your chain clean and shiny, will wash off if there's rain even in the forecast for next week. Any lube made for persistence in wet-weather use should be fine. I use and recommend Chain-L, made and sold by our very own FBinNY. You can buy it direct
here, and it's available on Amazon.