I am curious to know how a Dr Bristol is a fairly mild bit?
A Dr Bristol's mouthpiece is designed to position in the horses mouth with the bar in the middle of the mouthpiece to rest at an angle, where the edge of the metal bar is directly onto the horses tongue.
Where a French Link rests flat on the horses tongue, the Dr Bristol does not. So when the reins are pulled and the bit comes into effect - the edge presses down onto the horses tongue.
I would consider the Dr Bristol to not be a mild bit.