Can Bluetooth headphones work with Wii U?
Solution 1:
From what I've read, it looks like the Wii U does not support wireless headphones through bluetooth.
What you can do if you're able, though, is plug your wireless headphones (if they have an audio receiver attachment) into your T.V.'s audio output and then listen from there. Not all T.V.'s have this, so otherwise you are out of luck.