Thumb Drive .trash files

I have a Kingston 2GB Flash Thumb drive that I use to transport documents ans such between my iBook G4, the Macs at my high school, and my brother's Dell Desktop. It works fine, but as I move it cross-OS it fills up with .trash files that won't show up in the Finder or in Windows Explorer. I first noticed it because it said that it only had 1.5 GB of the 2GB open. This was weird because there was nothing to my knowledge on the drive. So I used GrandPerspective (a great app) and it showed that I had tons of .trash files that were invisible to both Finder and Windows Explorer. So I had to use Disk Utility to wipe it clean and restart it. However, I would rather not do this weekly (or so), and want to know if there is an easier way to delete them, or even make them stop happening.

I have before, and there have been times when the trash was never full and it was in and still showed these files.