Slightly distractedly, I went and connected 5V to the 3.3V pin on my DFRobot Bluno (the pins are right next to each other!)
The magic smoke leaked out of the AMS1117 3.3V regulator in a neat little puff. The sketch that was loaded on the board still runs fine, but the Bluno is no longer recognised by my Macbook Pro when I plug it into USB (I have tried different ports and different cables; they're all fine—it's the USB on the Bluno that's fried.)
In an attempt to repair it, I've replaced the AMS1117 (check the third paragraph of that tutorial—ha!) with an LF33ABV; this went well and I'm now getting a stable 3.3V on the 3.3V pin. Check out my handiwork:
However, the Bluno still isn't being recognised by the USB ports on my Mac.
Is there another way to upload new sketches to the Bluno? Theoretically you can do so over BTLE, but you need another Bluno to act as the "peripheral" and I don't have one to hand. I have various other Arduinos laying about if that helps.