The suggestion from Swaf might honestly be the only current option. I haven't purchased this adapter to confirm, but it appears that you can just use the pairing button on the adapter to connect your controller. Here are the instructions from the adapter manufacturer:
Turn on your Nintendo Switch, PS4, PS3, NEOGEO mini, or PS Classic system.
Connect the Nintendo Switch, PS4, PS3, NEOGEO mini or PS Classic to a TV. Just turn on your PC if you use the adapter on your PC system.
Connect the adapter into any spare USB port on your Nintendo Switch, PS4, PS3, NEOGEO mini, PS Classic or PC system.
To switch the modes, press and hold the button on the side of the adapter for 3-5 seconds.The LED indicator blinks slowly.
To sync the Bluetooth controller and the adapter, press the Button on the side of the adapter, and then press the SYNC button on your Bluetooth controller. The LED indicator blinks quickly. ** If the Bluetooth syncing failed, please connect the Bluetooth controller to the adapter using a USB cable (not included in the packaging, you can purchase it separately). As soon as the controller is identified by the system, you can remove the USB cable and start to SYNC it again.
The Bluetooth has been paired if the LED indicator lights up.
Your controller is now ready to use.
Here's a US Amazon Link for anyone that wants to test it (I'll probably be ordering one myself in a week):
https://www.amazon.com/Magic-S-Wireless-Controller-Adapter-Nintendo/dp/B081V8G1YX
With all of this said, it's not a perfect solution. The adapter only supports a single device at a time. And considering that many of us have bluetooth built into our PC's, it would be better to have some sort of pairing menu in BigBox itself to handle this. I don't know how it would be implemented, but if there was a way to access the Windows 10 bluetooth properties through a 3rd Party UI, it would be perfect.