So, it turns out @ogra was correct. Adding busybox to my snap’s staged-packages: allows it to run. Seems a little weird that there’s a hidden dependency for bare snaps, given that my app most definitely does not require /bin/sh or /bin/bash. IMO it should be judiciously added to bare or the dependency should be removed.
@cjp256 The bug you made says that it should force adapter: none, but /bin/sh seems to be required regardless of the adapter setting. adapter: none is already present in the snapcraft file.