If sound only comes out of one side of your headphones first look for the model of your headphones on the BTunes picker webpage http://thebtunes.com/pages/which-btunes. See that your BTunes is the correct model for your headphones, incorrect models will have audio problems and sometimes only play music from one side.
If your headphone matches the model of your BTunes and the sound still only comes out from one side there may be an issue with the device you are playing music from. If you are using a Windows computer to play music from make sure that the computer utilizes Bluetooth 4.0 and has the AAC and aptX codecs, with out these the computer will use old bluetooth technology to stream to BTunes and results in loss of stereo sound and also poor audio quality. If you are playing music from an Android, iPhone, or Mac these codecs come pre-installed.
If you are playing music from windows be sure that the high quality audio streaming is turned on for BTunes and not calling. Select listen to music to get quality audio from BTunes like shown in the screenshot.