I second the idea of wiping down and throwing on extra clothes outside. I started doing this because I wasn't sure if my co-workers were cool with tats, and wanted to get them covered up before heading in. Some fabrics are pretty good at absorbing sweat, which is great if you're continuing to sweat for another five minutes after the ride.

I wonder if anybody has tried rubbing alcohol in a spritzer bottle. It seems to be the main ingredient in many body deodorants - so you'd get the same thing, for cheaper, and without obnoxious scents.