How do I add an external Bluetooth antenna to this circuit?
As pointed out by Bimplerekkie, this is a hack, and might not be as efficient as the built-in antenna. But we can learn a lot from hacking, so why not try?
You can see a microstrip trace -- it's the wide PCB trace -- and it's probably about 50 ohms and would match the U.fl cable impedance well enough. There's a matching network halfway between the Bluetooth chip and the F-shaped antenna. Unsolder all the components from that cluster (I've marked in red). Next, scrape off the soldermask from the green patches, aiming for a footprint that will match the ground pads of the U.fl connector. Use flux, and tin the exposed ground pads, as well as end of the microstrip trace (blue square) where the matching network was removed. Put the U.fl connector on top, add flux again, and use a heat gun to reflow the solder. Pray. Try it!