From this forum:
I had this exact problem with my new d3400 as well. My settings originally showed Bluetooth ON and when I clicked on it, it showed a couple options: Network Connection-ON, Paired Devices, Send while off-"ON". I clicked on Paired Devices and it showed that it had connected to my phone today (even though my connection to snapbridge was unsuccessful) - so in an effort to retry my snapbridge connection I deleted my phone from the paired devices and this caused the Bluetooth on the camera to completely turn OFF and grey out. Same problem everyone here seems to be having where I couldn't even re-enable the bluetooth again and just saw an error message saying "option unavailable in current setting".
Alas, I found a solution - I have an iPhone 6 so for me at least this worked:
I went to bluetooth settings on my phone and went to the camera name and said "forget this device". I then deleted the snapbridge app and redownloaded it.
Then I went on the camera and tried to do the "connect to smart device". Instead of going to snapbridge, I went to my phone's bluetooth settings and chose the camera once the name popped up again. It prompted a pair message and I had to confirm the # on the camera matched the # on my phone. It then paired successfully and the bluetooth on my camera was back on! -- (disclaimer.. while this was great to see that at least the bluetooth was on again, this did not resolve the issues I was having with snapbridge - I still can't seem to get it to connect through the app, but perhaps it will work out for others..)