The wattage of the Internet Bridge is approximately 0.7 W, this adds up to 6.21 kWh per year. Hypothetically, if you have an average electricity price of €0.22/£0.18 per kWh, this results in yearly expenses of approximately €1.37/£1.15.
Note: If you disconnect the Internet Bridge, your tado° devices will constantly search for an Internet connection and their batteries will deplete much faster. tadoº devices are designed to remain connected to the Internet Bridge and use charged batteries, so your heating system may react unexpectedly if you disconnect it for a long period of time or disregard low battery notifications.