As I'd previously mentioned, I'd had issues with a USB 3 drive enclosure when trying to set up a backup drive with Bitlocker on Windows 7. When I replaced the USB 3 enclosure with a slower, USB 2 enclosure, I found exactly the same problem. On trying to enable Bitlocker, I got the message: "A drive attached to the system is not functioning."
Hmm. What I discovered is that if I tried a different Bitlocker partition size, e.g. 307275 MB rather than 307200 MB, it worked! There were no other partitions present on the drive; this NTFS partition was the only one.
Furthermore, this "fix" applied to the USB 3 enclosure, so it seems it's an issue with my drive (Samsung ST1000LM024) or Windows itself.
It's a really peculiar issue: partition sizes of 307200, 307250 to 307255 and 307265 to 307269 MB gave me this error, but a 307270 MB partition would have been fine. Likewise, I got errors at 153600, 460800 and 76800 MB; it certainly doesn't like multiples of roughly 150 GB... (it's possible that this is a red herring though — I couldn't realistically try every possible partition size).
I haven't observed any other issues having setup the drive, but this is unusual nonetheless, and I couldn't find anyone documenting anything similar.