Rain bike!

worrying about it and not riding is surely worse than riding and wearing out a few parts a little bit sooner.

What's a bottom bracket cost? Unless your riding Campy (and for that I have sympathy for your pocketbook) 20-35 bucks? and chains? 15-30 bucks, unless you've been suckered onto 10 speed, and for that I have sympathy for your pocketbook as well.

Rain bike! and don't worry about it.