MileIQ will work regardless of whether Bluetooth is on or not.
Having Wi-Fi on, however, is highly recommended. Even when you aren't connected to a Wi-Fi hotspot (i.e. your local coffee shop), your phone uses the hotspot proximity (and if you live in/near a city, you pass thousands of them a day) to register location information. Wi-Fi is far more efficient on batteries than other location sources like GPS.
If it is not already, please enable WiFi by going to: Settings > Wi-Fi > On.
Additionally, please check our Drive Detection best practices with MileIQ article. Making sure everything is set up correctly will ensure the best performance with our service.