@
Kithas
Your explanation is missing something. When you use something as/like an improvised weapon, it becomes a weapon (to you). So you can't say you are dual wielding two shields as weapons and gaining the TWF benefit and be able to use BB/GFB, while simultaneously stating it is not a weapon in order to gain the benefit of the Dueling Fighting style on the same turn.
Same with sword and board. When you attacked with your sword and used the benefit of the Dueling fighting style, you can't simply switch within your turn and say: "The shield is now an improvised weapon and I attack with it as a bonus action and TWF."
So either you do your attacks with your sword only and benefit from Dueling, or you use both sword and shield as weapons and profit from Dual Wield and TWF. But not Dual Wield, TWF and Dueling all rolled into one.