I saw her... biking in the rain!
Yes, you might get a little wet, however, if you have some rain gear that you normally wear walking in wet weather, you can wear it on your bike too. Some individuals in Northern Europe even carry umbrellas while cycling. For the ladies, boots and tights under a raincoat present a practical solution.
Some tips though - you should make sure your breaks are nice and tight and you might want to invest in some fenders and a chainguard. My left (non-rolled up) pant leg got sprayed with some wet grease last night.
I was nominally wet when I got home, but honestly it made me feel young again, getting irresponsibly trapped in the rain, and then quickly changing into my dry cozy pyjamas.