Are there any privately owned bridges in western democracies?

Of course there are! If you don’t believe it, look up the definitions for “bridge” and discover what can result from asking a vague question.

But think about it. Are there any privately owned roads or trails or paths in Western democracies? Are there any privately owned roads or trails or paths crossing streams, gullies, depressions, etc.?

That expression ”...a bridge to sell…” is a reference to the gullibility of the “you” in the expression. The “bridge” in the expression is usually understood to be the Brooklyn Bridge, meaning the person would be gullible enough to believe someone has the authority to sell them the Brooklyn Bridge.

Traditionally privately owned bridges and highways in the US are toll bridges.
https://en.wikipedia.org/wiki/Dingman's_Ferry_Bridge

It won’t link otherwise.

Bridges for railroads are owned by the railroad.

Thanks @Yetanotheruser and @ibstubro and @Tropical_Willie.
So, is the saying is no longer valid?

On the contrary, the saying is still valid. I’ve usually heard it said something like:

”...and if Joe believes that, then I have a bridge to sell him!”

This would indicate that the speaker believes Joe is extremely gullible and would believe almost anything he was told.

@Yetanotheruser There must be a miscommunication

It’s a common expression because it was assumed that only the most ignorant and gullible of people would believe that a single individual owned the Brooklyn bridge.