I'm not a native speaker, but doesn't "entre" sound more like "between" than "across"? How about "sobre"?

@morbrorper. I agree with you, "sobre" is the right word. Unfortunately I cannot edit the sentence anymore because it has an audio.

If grammatically correct, disconnect it, and write a new one what matches with the English.

Does "...entre cada río" still make sense as its own sentence?

I wrote "...sobre..." here [#9769425], could you adopt it?

"... entre cada río" sounds a bit illogical, if we are talking about road bridges.

@arh Do you think this is a proper sentence?

Como teskmon ya ha comentado, lo apropiado en este caso sería:
- Había un puente sobre cada río.
A mí también se me pasó al grabarla.

@CK
Can you delete the audio so it can be edited, please?

--> Había un puente sobre cada río.

@arh

Should this audio be deleted, or moved?

@CK
Deleted. I'll record it again once the sentence is edited.