Well, I gave up on this and sent the controller back to Amazon. I then took my wife to Gamestop to buy a second Wii U Pro Controller, which is, by far, the best and most reliable controller for Retropie (that I've experienced, anyway).
@mitu OK. I tried what you suggested and paired it with my Windows PC first. It paired right up without any issues. I then moved to the Pi. Before I started pairing with it again, I first removed the 8bitdo Bluetooth controller, updated to Retropie v 4.4 and then rebooted. This time it recognized it and paired up with it without issue but just like the first time I got it to successfully pair up, it didn't seem like any of the buttons would work when I went to configure them.
When I go back to check Registered/Connected Bluetooth Devices, it shows the Quadstick is registered and gives its MAC number but doesn't list it as active in active connections.
If it is registered and connected, and I'm trying to configure the inputs, should it not be active? Or does it not become active until after the inputs are set?