You shouldn't be getting a dialog box at all, and I'm not sure what you're doing that is causing that dialog box to open.
And you shouldn't be bouncing anything at all before you do this. You don't need to have Logic open on the old computer (or, while you're copying, on the new computer for that matter). You just need to copy the entire folder via the Finder. i.e. drag the entire project folder (which will have an Audio Files folder, a Bounces folder, and a Logic Song File icon inside of it) to your La Cie, then connect your La Cie to your iMac and copy that same folder to your iMac.
Once you copy the entire logic project onto your iMac, you should be able to simply double click on the logic song file, and it should open. Or, if you have an earlier version of Logic on the iMac as well, drop the song file icon onto the Logic Studio 9 icon, and that will force it to open in 9, then you can save it as a Logic 9 project.
Of course, this may go without saying, but the Logic file is the one that looks like a little keyboard, or a little preview of the arrange page. That's the file you double click on.