I bike most places. There's good access and good parking at my university, so on bad weather days, or when I'm late, I take the car.
My problem is sweat, as much as rain. After biking for 25 minutes I absolutely need to change my shirt. This is fine for everyday use, since a sweater or polo fold nicely in a backpack, but for business meetings (I'm halftime student, halftime PM), I need a suit-coat and a shirt, and they'll wrinkle way too much in a backpack.
Suggestions?
If you do not have shower facilities, a reasonable proxy is to wait until you've stopped sweating (usually 10 min. post-ride) and clean up with unscented baby wipes in the bathroom (and if needed, use a travel bottle of shampoo to rinse sweat out of your hair). The rule is try not to pack what you can leave at your destination (towels, clothes)
Most bike commuters I know bring batches of clothes to the office and/or wear sweat-wicking business casual (Nike's golf apparel or cheaper). Hopefully you might be able to store a suit/pants with a colleague? They discuss and dissect bike commuting on Bike Forums endlessly. http://www.bikeforums.net/forumdisplay.php?f=20
I've seen garment-bag-style panniers that hang over both sides of the rack. In my experience, rolling clothes (with that which is most likely to wrinkle on the outside) leaves them far less wrinkly than folding them. It may be worth a try.
Also, I ofter hear of people bringing all of their formal clothes on Monday (whether driving or by e.g. bike trailer) and leaving them at the office through the week.
I have a trifold garment bag with backpack straps, and internal padded straps to keep clothes in place. I keep a change of shoes at work. I also have a vest filled with a liquid that freezes at 50 degrees F, to reduce the sweat (I got it at 50degree.com, years ago, but you can probably find it cheaper somwhere else). It's not a perfect solution, but those both help.
