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I'm also in the category of having a snap on my primary, with that said a couple options if you don't.
1. Just hold it in your hand.
2. Tuck it under your shoulder strap.
I would think the bungee idea is good when with a buddy also in case of separation or the time it takes for the buddy to realize you are unconscious. I haven't heard of any others anywhere doing this.
When you don't have your regulator in your mouth, what do you do with it?
Secure it to the shoulder strap of your BCD? If this is the solution, what are your favorite methods of securing it?