Originally Posted by CoachJamesEwart
This bobbing motion is more pronounced in the one arm drill because the opposing arm is down at your side and not extended. When the opposing arm is extended, it supports the weight of the recovering arm and damps the bobbing. If you look at the film of Terry doing the one armed drill you will also see a pronounced bobbing, as ZT has already pointed out.
In real freestyle, the opposing arm is extended and this effect is more subtle, but it is still there.
You should not be bobbing and certainly not be using the aforementioned Bob to help you breathe.
I don't like the one armed drills for freetstyle in any of its form actually but if you find benefit in it then of course use it.