Do you see a Bluetooth device successfully installed in Device Manager?
You may need to reinstall the latest Bluetooth driver for the 6235 card. It's available here: https://downloadcenter.intel.com/Detail_Desc.aspx?agr=Y&ProdId=3502&DwnldID=22860
I must have "forgotten" to install those drivers... Excellent answer, thanks for the direct link!
Now I only need to be able to get my Samsung HS3000 Bluetooth stereo headset to work in stereo on the NUC...