Some firmware implementations have problems booting from a GPT disk in BIOS mode unless the protective MBR is modified to include a "boot flag" on the 0xEE partition. I describe this problem in more detail here.
That said, I don't know offhand if the Fedora live CD, installed to a USB flash drive, would have that issue. I do know that Fedora uses an extremely weird partitioning layout to make it work on both CDs and USB flash drives, and in both BIOS and EFI boot modes, and on both PCs and Macs. With all the contortions involved, it's inevitable that some systems will "fall through the cracks." IMHO, they'd have been better off creating multiple images for different types of computers.
It's conceivable that you could use UNetbootin
to create a new disk image that would work better, but I can't be positive of that. It's worth a try, though.
Why do you want to boot in BIOS mode rather than in EFI mode? There may be some way to accomplish your goals that would work using an EFI-mode boot, if you can't boot in BIOS mode; or you might be able to do it with some other product that doesn't support EFI-mode boots at all.