I would think that the "bridge" or center line concept is really not the first link in the chain.
The first link in the chain is to attack first (ideally) and do it on a straight line to their head or something else juicy on the center line of their body. Only if they block that somehow do you start working the "bridge".
So against someone who "yields the center" and attacks from the side (like boxing hooks or what have you) then the real solution (if you want to stay inside a tighthand bridge/center line style of fighting) is to attack more aggressively up the center. It is worth mentioning this will be a dreamy (in the sense of one getting KOed) experience if you haven't got the chin or ability to cover/absorb those hard hooks and what all to your cranium and/or chin.
Basically if you try to "to and fro kickbox" with a shorthand bridging style I'd think you are already missing the point.
The point of that shorthand bridging stuff is to attack first and KO them so fast they never get the chance to attack from the side. You attack so fast the only thing they can do to avoid the KO is to get their hands up on their center line and contend with you there. And then you have all the fancy centerline/trapping type stuff to deal with THAT eventuality.
If they start from far enough out that they pop off first I'd suggest jettisoning the "tighthand/center line stuff" and just driving in to clinch where you can use short-range trapping stuff like elbows.
My .02$.
"The first stage is to get the Gang( hard, solid power). every movement should be done with full power and in hard way, also need to get the twisting and wrapping power, whole body's tendon and bones need to be stretched to get the Gang( hard) power. "
-Bi Tianzou -