I think “Never Goin’ Back To Georgia” by The Blues Magoos might qualify.
Roy Orbison was the master of weird song structure. “Running Scared” is just a slowly intensifying narrative verse until it gets to something that sounds like a bridge, but is, in fact, the finale.
Regarding “Pinball Wizard” … I’d regard “That deaf, dumb and blind kid / Sure plays a mean pinball” as repeated lines that end the verses, as opposed to a distinct chorus.
“Pinball Wizard” also does have a coda, but I didn’t conceive of it as a bridge since it didn’t return musically to echo an earlier part of the song (hope that makes sense to those that know the proper terminology). The strumming between “But I just handed my pinball crown to him” and “Even on my favorite table / He can beat my best” seems really brief/quick to serve as a bridge, but I can see someone making the argument.
“We’re Not Going To Take It” is a weaker case for fulfiling the OP. I had looked through the lyrics before proposing this song, and noted that there wasn’t a word-for-word repeating chorus before the “See me / Feel me” portion. However, there is a clear instrumental refrain with close sound-alike lyrics (“Gonna break it / Gonna shake it / Let’s forget it better still” and “We forsake you / Gonna rape you / Let’s forget you better still”). I can’t argue too vociferously that those parts aren’t choruses.
Once “See me / Feel me” starts, I regarded that as repeated verses – does the repetition instead make it a repeating chorus? Perhaps so.
After that, I considered “Listening to you / I get the music” portion, through to the end, as pure unrepeated verses.
Isn’t the “How do you think he does it?…I don’t know…what makes him so good” bit the bridge?