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.