I have a specific USB thumb drive for backups. I'd like to know which options I have to detect when this thumb drive is inserted and execute a BASH-script. And I'm interested in which way you recommend.
You might want to look at the HAL/Udev events framework
This article explains how to get scripts and programs to run on HAL events such as a new USB device being added.
That being said, any modern Gnome desktop allows you to set actions for before automounting of new volumes.