You can turn off your cellular signal and WiFi but Bluetooth has to remain enabled for the headband to send data to the app. Unfortunately, Muse doesn’t store any data directly on the headband, as most other sleep trackers do.  On iOS, you can enable airplane mode and then go back to the Control Center and make sure Bluetooth is turned on. Once you’ve done that, iOS will remember this setting and keep BT on whenever you enable airplane mode in the future.