First, check to see if your headphones are compatible with the Peloton Bike. To pair your Bluetooth headphones, put your headphones in pairing mode. Most headphones flash a blue light when they are in pairing mode (check that your headphones are not connected to any other devices before pairing).
Next, log in to your Bike and click the menu button on the bottom right corner of your home screen. Find the Bluetooth settings on the left-hand side of the screen. Toggle the Bluetooth setting to "on" to have your Bike search for and connect to your Bluetooth device.
You can also refer to the following video for assistance pairing your bluetooth headphones.
If you are having trouble pairing your headphones, please contact Support here.