To talk about something in a loose or gossipy manner. A noun or pronoun can be used between "bruit" and "about." They are bruiting about that story as if it's the truth. Management is just casually bruiting about the idea of layoffs. Don't bruit that nonsense about here, we're not buying it.
bruit something about
to spread a rumor around; to gossip something around. You really shouldn't bruit that incident about, you know. The story was bruited about all over the office.