The PI Hardware is dual mode, but wasn't originally set up for BLE by default. I believe that the support package needed to do this is "BlueZ" and you may need to build a non-standard version and install it to play with this.There are some examples on YouTube and elsewhere.
I got as far as using pi shell commands to enable BLE, but never got it working reliably with other equipment and haven't had time to get back to it.
The situation is complicated now that the PI GUI takes over control of Bluetooth for its own uses. I don't know if you can get BLE working without disabling the Raspbian use of it for keyboards, mice, etc. which is now enabled at bootup.
Depending on what you are doing, you may also need to get it running as a "slave" instead of it's usual role as a master on the pi.
Try googling BlueZ and BLE and PI together. There's a lot info out there, but much of it is out-of-date...
hope this helps a little - it would be great to see it working, since the PI Zero is easy to work with for building very powerful peripherals...
M