Welp, I found where it came from.
I had the car up doing front discs and pads and noticed a bright, clean ring reflecting at me from the darkness. Low and behold, I found the location of my broken bolt.
It's one of the bolts holding on the electric power steering assist. And, judging by the bolt, there must be some length of it still stuck way inside.
I'm going to gamble on not *really* needing it. It looks like it's just holding on the power steering assist, so even if it fell all right off, I'd just be left with no power steering, right? Not the worst thing in the world if you ask me.
***EDIT***
Also, it looks like this is a common F series problem including MY 2014-2016 228i:
https://f30.bimmerpost.com/forums/sh...1469927&page=3