Nope Bluetooth is ok during a flight.. from the FAA:
> Passengers will eventually be able to read e-books, play games, and watch videos on their devices during all phases of flight, with very limited exceptions. Electronic items, books and magazines, must be held or put in the seat back pocket during the actual takeoff and landing roll. Cell phones should be in airplane mode or with cellular service disabled – i.e., no signal bars displayed—and cannot be used for voice communications based on FCC regulations that prohibit any airborne calls using cell phones. If your air carrier provides Wi-Fi service during flight, you may use those services. You can also continue to use short-range Bluetooth accessories, like wireless keyboards.
https://www.faa.gov/news/press_releases/news_story.cfm?newsI...
Airplane mode has two reasons. One reason is because at one point your cell radio risked doing unpleasant things to cellular ground stations, and another reason being that the FAA wanted you to pay attention to your safety demonstration.
Bluetooth was allowed on planes quite some years ago.
Another reason to turn on airplane mode – or at least disable mobile – is that your phone will keep searching for a network tower when it's out of reach, which will drain battery quite a bit faster.