Not all Single hands free stream music. Look at the info/packages of the ones you are considering. I just bought one myself for hands free and music. I wanted a cheap one, as I already have a great set of bt headphones. I could not find any of the cheap ones that do it. I spent $59 at BB on a BlueAnt. Works great
The headset has to support a2dp.
I would love to hear (read) the explanation for why long-term use of a single ear headset playing music can cause ear damage as opposed to headphones not causing the same damage to both ears.
Don't bother with single ear. Get the jaybird f3. Great sound and won't go anywhere while you run. Sound quality is defined enough to listen to classical music and still hear cars and other peds.