Ok I think I might have figured out my own problem, or at least a work around.
So my main editing PC is a gaming laptop (Acer VN7 792G) with the following specs:
Intel Core i7-6700HQ CPU
16 GB of DDR4 RAM
Integrated Intel Graphics HD 530 (shares system RAM)
Nvidia Geforce GTX 960m with 4 GB of GDDR5 VRAM
With these newer gaming laptops, they have two different video cards; an integrated card and a discrete Nvidia graphics card. I use this laptop as a desktop replacement and I have it plugged in 95% of the time. So I changed the global default graphics card to the Nvidia card. This was very helpful because it significantly decreased file production times. However, AVS Video Editor would not create my Blu-ray menu files when using the discrete Nvidia graphic card.
Today, I opened AVS Video Editor with the Integrated Intel Graphics HD 530. It took longer to produce the files but, it worked correctly. The .m2ts menu files were created and worked.
So even though I have found a work around. I would still like to find out why I cannot use my Nvidia GTX 960m to produce my Blu-ray files.