I would like to be able to discover other iOS devices over Bluetooth while my application is in the background. Is it possible to use Bonjour or Game Kit to do this discovery while my application is not in the foreground?
Would it be possible to do this and fire off a notification if a compatible device is discovered?
Also, would I be able to run in the background while playing audio and do this detection?
This is not possible while your application is suspended. From the iOS Application Programming Guide:
Cancel any Bonjour-related services before being suspended. When your application moves to the background, and before it is suspended, it should unregister from Bonjour and close listening sockets associated with any network services. A suspended application cannot respond to incoming service requests anyway. Closing out those services prevents them from appearing to be available when they actually are not. If you do not close out Bonjour services yourself, the system closes out those services automatically when your application is suspended.
Be prepared to handle connection failures in your network-based sockets. The system may tear down socket connections while your application is suspended for any number of reasons. As long as your socket-based code is prepared for other types of network failures, such as a lost signal or network transition, this should not lead to any unusual problems. When your application resumes, if it encounters a failure upon using a socket, simply reestablish the connection.
However, if your application is streaming audio, it would be necessary for it to maintain network connections, so you should be able to do Bonjour discovery while in the background for an application continuously playing audio. Make sure you don't abuse this by playing a silent audio clip in a loop just so that you can stay in the background, or your application will be rejected.