Depending on which Garmin HRM that you have, you may need to double check that it broadcasts via Bluetooth. I had the same issue with my HRM and ended up buying a Tickr as it solved the issue indoors. Still use my Garmin HRM outside with head unit.
I have a Tickr, and it connects just fine to my iPhone and my iPad. Just keep in mind that most devices can only connect to one device at a time using Bluetooth.