What makes a USB device bootable depends on whether the system is using legacy BIOS or UEFI, but in both cases the firmware must find valid boot structures on the device.
In legacy BIOS mode the USB must contain a valid MBR in the first 512 bytes. That MBR must include executable boot code and at least one active (bootable) partition. The BIOS itself does not understand filesystems; it simply loads and executes the boot code found in the first sector. If that code is valid and the partition table looks correct, the device is considered bootable.
In UEFI mode the process is different. The device must contain an EFI System Partition formatted as FAT32, and inside it there must be a file such as EFI/BOOT/BOOTX64.EFI for amd64 systems. UEFI firmware looks for that file and loads it directly.
If a USB device appears in BIOS but does not boot, it usually means the boot code is missing or invalid, the partition is not marked active in legacy mode, the layout is incorrect, or the image was not written properly. Simply copying files to a USB stick does not make it bootable.
If the USB device does not appear at all, it can be due to firmware limitations. Some BIOS versions only recognize devices that present themselves as USB hard disks. Some sticks identify themselves in unusual ways and are not handled correctly. The partition table may be corrupted, or the firmware may fail to initialize the device early enough during startup.
Seeing the device listed in BIOS only means the firmware detects it as storage. It does not guarantee that it contains valid boot code.
The most reliable way to make a FreeBSD USB bootable is to write a proper memstick image directly to the device using dd, which ensures the correct boot structures are present.