GIMP can load and save images which have been bzip2 compressed. To save a bziped file, you can either use Save By Extension or bz2. You need to name your file in the format filename.extension.bz2 where extension is an extension for a supported file format. For example, to save a bziped TIFF file called foo, you would enter foo.tif.bz2 as the filename.
For this plug-in to work you need bzip2 — you can check if you have this by typing bzip2 --version at a terminal window. If you get bzip: command not found or similar, you don't have bzip2.