There are three things I’ve always wanted to do but never taken time to ask as a proper Feature Request :

I’d love Bridge to be able to invert a filtered view:
Say I picked all my red labels, with 4 stars and more, mainly squared pictures.
Now I want ALL the OTHER pictures.
It means picking NO label + green and blue + ALL other formats.
I’d love to do that in 1 click, even if that click is under a menu :)
I’m thinking of the hamburger menu of the filter panel,
The filter icon on top right of the main content view,
I’m also thinking of the contextual menu like right click in an empty space of the filter panel or the content panel.

Other thing I want is, in the filter panel, an “exclude” state to the checkboxes.
Right now, checkboxes work as OR, I would love them to have a NOT way of working.

I want pictures with women but not one woman only.
Or a truck AND a person but NOT an animal.

I know I could alt click to select all other results but as you know Boolean logic, this is not the same thing :)

Last thing in that direction would be OR and AND filtering in one category, mainly keywords (you cannot be landscape AND portrait, but you can have a person AND a car).

Let me know if that sound correct and/or if you’d see that in Bridge.

I added a file with :
1. full folder
2. my selection (red labels and 45)
3. what I get by alt-clicking every checkboxe
4. what I'd want as a "invert selection"

It's easy and obvious on a 12 photos set, you can imagine the time consumed on a bigger set.