A bridge, in probably its coarsest definition, being a basic:
verse/chorus
verse/chorus
bridge
verse/chorus
structure, also has variations, like - maybe one less verse/chorus.
This can get problemmatic when dealing with annoying prog numbers comprising eight trillion different parts, and so, it’s like - which part’s the freakin’ bridge?
Also, is there such a thing as an instrumental bridge that does not have a solo in it? (talkin rock and pop, here) I would consider that a challenge, and the best I can come up with is this.
I was hoping to use this, but would it be agreed that that’s more of a refrain, because it appears again in the song?
In classical music, wiki mentions bridge-passages. I would like to see some posts pointing out to me where the bridge-passages are in the more well-known pieces like Eine kleine Nachtmusik, some of the Beethoven symphonies, Thus Spoke Zarathustra, etc.
I like the bridges in Making Plans For Nigel and Niel Young’s cover of Don Gibson’s Oh Lonesome Me. (In the latter, I really like the backing vocals that eventually join in. Crosby’s?) (Stills does backing vox elsewhere, but here, the “burliness” of the vox makes me lean more toward Crosby.)
Heh - so is this the bridge in Cream’s Badge?
Anyhoo - any reach out to you that say “hey, what an awesome bridge I am”?
“Where’s that confounded bridge?”
No crunging.
In popular music, “the bridge” is a stereotypical section that shows up in the same way in the same place in nearly every song. Classical music doesn’t have “the bridge” in this predictable way, because classical music is much less rigid in format. Not that classical music avoids formula - there’s formula all over the place - but classical music has a huge number of truly different formulas, while popular music basically sticks to just the one you showed. So looking for “the bridge” in classical music is a bit like arriving on a far-off inhabited planet, getting out of your ship, and looking for their 1940s-style diner. They probably have many kinds of food, but you’ll have to look at their food for what it is, rather than stand around wondering why there’s no diner. 
Missed edit window:
But to find A bridge (as opposed to the bridge) in classical music, listen for some of the same things you’d listen for in popular music: a part with some odd-sounding or contrasting harmony, then leading back into a familiar part.
As already stated, classical music has bridge-passages:
That’s more or less a metric I try to go by when listening to classical music, and of course wiki goes on about different kinds of bridges and theme transitions and enharmonic and chromatic modualtioins, which I’ll admit is starting to get a bit out my wheelhouse, heh.
Funky, brief instrumental bridge in Burning Down the House and a velvety cool one with Elvis Costello’s Shabby Doll
… and it’s not the same thing, and you don’t normally spend time looking for it in every piece you listen to. Bridge passages in classical music are often insignificant, or might not even be part of the form of the particular piece you’re hearing. They certainly don’t hold the universally important position that “the bridge” in pop music does.
Sure, I get it that the bridge has different manifestations (other than just the bridge-passage) as well as varying levels of significance and relevance to any given classical work; I’m trying to get an idea (through youtube cites) of these different manifestations, along with aforementioned theme transitions and enharmonic and chromatic modulations - my ignorance could use a good tolchoking, there.