Hopefully this will help someone else with a similar problem.
I just received an Intel Compute Stick, model number BOXSTCK1A32WFCR with version 18 BIOS, and wanted to update the BIOS before upgrading to Windows 10.
However, when I put an SD card with the .BIO file into the ICS it was not listed in the available media; only the EFI partition was listed.
I tried rebooting a few times to be certain that it wasn't just a one time fluke, and checked that the file was indeed in there once I was booted into Windows on the same system.
A couple of hours of Googling and I didn't see anything in regards to issues while updating the BIOS.
Then it dawned on me that all of my external media is formatted in exFAT, and just maybe it can't read it.
I dug up another SD card and formatted it in FAT32, copied the .BIO file to it and the media showed up just fine.
I did not try NTFS, and maybe another version of BIOS can read exFAT. It just so happened that the version that was on my device when I received it could not.
BIOS update was smooth sailing after that!