iOS how to stream audio to a bluetooth speaker - ios

Question

I want to stream my voice with my iPhone 4 (iOS 7) to a Bluetooth Speaker Device (this one) with the lowest latency/delay possible.
I managed to capture my voice with almost no latency and broadcast it to my speaker through an audio Jack connector but when I pair my Iphone with my Bluetooth Speaker Device it doesn't work. I don't hear anything.
And when I open Youtube in my iPhone the sound is correctly transmitted to the bluetooth Speaker Device. So the problem is not in the Bluetooth Speaker Device but in my code.
Do you have any suggestions or advices ?
Here's the code I put in the delegate class (didFinishLaunchingWithOptions function) to init the audio session :
// configure the audio session
AVAudioSession *audioSession = [AVAudioSession sharedInstance];
NSError *err = NULL;
// deactivate session
[audioSession setActive:NO error:&err];
if (err) {
NSLog(#"There was an error deactivating the audio session");
}
[audioSession setCategory:AVAudioSessionCategoryPlayAndRecord withOptions:AVAudioSessionCategoryOptionAllowBluetooth error:&err];
if( err ){
NSLog(#"There was an error creating the audio session");
}
[audioSession overrideOutputAudioPort:AVAudioSessionPortOverrideNone error:&err];
if( err ){
NSLog(#"There was an error sending the audio to the speakers");
}
// Activate the session
[audioSession setActive:YES error:&err];
Then I use EZAudio framework to send audio to the audio device:
/**
Start the output
*/
[EZOutput sharedOutput].outputDataSource = self;
[[EZOutput sharedOutput] startPlayback];