Don't know anything about Bridge in Math, but sounds like fuzzy math to me... Any teacher who sticks to only one prescribed way of thinking is doing kids harm.
But in general I have huge problems with visual-based math. It works well for some kids to a certain point. But it doesn't work well for everyone. And fundamentally, math is a thought process that involves a huge deal of abstraction.
Hah, you've stated some of my top concerns here. Especially for my DD, who is a concrete thinker and non-visual and not at all pleased when asked to produce a bunch of diagrams on paper of something she is already sure she 'gets'.