That's how I eat them too. And once I get to the folded half of bun, I start ripping off pieces of it so all that's left is the piece between my two fingers.

Another technique that works well is to manipulate the burger so it slides up out of the bun. This is a lot harder to explain. You sort of "squish" it up and out, leaving behind the bun.

Talk about traumatizing the teens! LOL.
I was at a farm fest, and when I ordered the polish sausage I asked if I could see the bun first. The teenager gave me the bun, then was MORTIFIED when I proceeded to remove 90% of the bread from the bun. I gave it back to and said "OK, now you can put the sausage on".
It was like I had three heads.