There's an option to "Backup" within one of the menus on Picasa. When you sleect it there are prompts for what you want to backup & more importantly to where, in yoru case the USB stick.
This doesn't simply put a copy of each photo on the stick it puts I imagine a compressed archive of your Picasa setup. Should anything happen to your laptop/PC that has PIcasa setup you can re-create using this "backup" file.
This may help: http://picasa.google.com/support/bin/answer.py?answer=18393