I use the RokSak. They make a specifically tailored bass case for Thunderbirds. I've been using them for several years now on many instruments, and I have nothing bad to report. Lots of pockets for other things too, like cables, sheet music, even a mobile phone slot.
Can't find any exact pictures of the case online, only older versions and cases that are the same but a different shape, so I will describe. The case has decent padding around most of the bass, including a neck support with Velcro strap to hold it down. The bag now is mainly a sleek black with blue zips for the accessory pouches. Even though it's padded well, the case remains fairly flat, so you can easily stack other basses or amps next to it. I've had some where the pockets stick out making it hard to put things next to it in the car. It should be an easier piece to deal with when playing Car Tetris, ha ha.
Overall, a good product that I would definitely recommend. Got mine for £35, don't know what that will be in any other country but U.K. But it's worth a look. Just put RokSak Thunderbird Case into google, and your should find it somewhere.