Bluetooth is only active on the Oura ring for short periods of time, well below 1% of the day. Data is transmitted more continuously when the ring syncs with the app and during firmware updates. Additionally, the Bluetooth signal and advertising are turned off when you're inactive or sleeping.
The limit for SAR (Specific Absorption Rate) for a device such as the Oura ring is 2.0 W/kg for head and body. The Oura ring's SAR level is 0.0003 W/kg (read the full SAR Compliance Test Report here).
However, if you prefer to keep the ring's Bluetooth off completely, you can enable Ring Airplane mode.
Note: To sync ring data with the app, airplane mode needs to be off and Bluetooth needs to be enabled. To turn airplane off, connect your ring to the charger. Otherwise, airplane mode stays on for 7 days at a time if you have the iOS app. On Android, airplane mode stays on for 24 hours at a time.
The Oura ring is a Bluetooth Smart class 2 device which has adjustable output power; 2.5 mW at maximum. The ring uses lower power levels, typically 1 mW. In comparison, the output power of a cell phone is typically 1000-2000 mW peak and approximately 120-250 mW during a call (source: Wikipedia).