This took a long time to figure out. Here are the basics;
The NUC arrives with [ Intel(R) Centrino(R) Advanced-N 6235 ] its a dual Ethernet Card and Bluetooth Adapter.
When you install the Ethernet drivers, it does not install a Manufacturers driver for the Bluetooth Adapter, instead it installs a generic Microsoft driver which does not include Bluetooth Profile Providers for the various functions of the device. Thus you could pair a headset with the adapter, it would show up in the Devices and Printers section, but it would have no profile providers and not appear as an audio device.
The fix is to find a complete manufacturers Bluetooth driver with Profile Providers and then pair the device.
TLDR - get the Lenovo
Its large, 298 MB but its worth it.
It comes from 2013 but it does install, separate and side by side to the existing and working Ethernet driver and it installs a complete set of Bluetooth Profile Providers.
A few tips;
Any pre-existing paired devices will not be "fixed" simply by installing this after they are paired and showing up in the Devices and Printers.. you have to remove them, reboot and pair again.
During the install there is an EXE and an MSI phase.. so it looks like its installing multiple packages using multiple methods.
After package install and pairing, Device Manager will show an anemic looking "Bluetooth Audio" device, which is a little odd for a Bluetooth device the Bluetooth Profile Providers don't usually show up in Device Manager.
All oddities aside this Lenovo driver package seems to follow the Bluetooth design guidelines to a "tee" and integrate with Windows 7 x64 very well.
When downloading from Lenovo, it will popup a box asking for a Serial Number, lots of text .. ignore all of it. Go to the very bottom and click [Cancel] and a banner will appear over the same page you were launching the download from. It warns this software may not work with your hardware - click the download link again, it will begin downloading.