As you probably figured out, my problem with the Buffalo USB 3.0 External Blu-ray not being seen by CDBurnerXP was in the Data burning mode. At your request, I tried Audio burning mode and CDBurnerXP DID successfully see the USB 3.0 External Blu-ray drive. But, while in Audio burning mode, when I went to Recorder > Device information, only information selection was available for the built-in CD/DVD drives. After that limited success in Audio burning mode, I tried the Data burning mode again, but no luck seeing anything but the two internal SATA CD/DVD burner drives.
For the record, my version of CDBurnerXP is 18.104.22.16868.
I did one other test. I have a laptop with one built-in CD/DVD burning drive. I plugged the Buffalo USB 3.0 External Blu-ray drive into the laptop and the Data burning mode only displayed the one built-in CD/DVD burner drive. A test of Audio burning mode succeeded in seeing the USB 3.0 External Blu-ray drive, but still nothing changed for the Data burning mode.
Finally, I installed the CyberLink Media Suite software [which with the Buffalo USB External Blu-ray drive]. It successfully burned in Data burning mode on both my desktop PC and the laptop.
Your assistance will be greatly appreciated.