In principle, "our collective ass" means the (necessarily figurative) ass of the group as a whole, as opposed to the (literal or figurative) asses of the individual members of the group. In practice, however, I don't think the sentence would really be taken any differently if "our collective ass" were replaced with "our asses". I think "our collective ass" was mostly chosen for the humorous image of a shared ass. (The word "collective" is essential for conveying this image; just "our ass" would be confusing at best.)
Is that use of word "collective" a regionalism?
The word itself certainly isn't, and I'm sure that English speakers from many different regions would get both the meaning and the humor; but it's possible that this bit of stock humor is more common in some regions than others. It's certainly colloquial, though; a bit slangy, even.