The Verge notes that the BSOD occurs only with the iPhone 5s and is usually caused by Apple's own iWork apps. As you can see in the video below, the error can be triggered by multitasking between those apps.
One suggested workaround is to disable iCloud syncing for Pages, Keynote, and Numbers.
Take a look below to see the error triggered. Apple has yet to comment on the issue but there are several Apple support threads on the problem.