throw a bridge +preposition
has seen usage.
The phrase goes back at least 150 years.
The Brooklyn Bridge: A Cultural History
More recent usages...
North Dakota's thundering economic boom (when I was driving across the state last fall, almost all the local radio announcements seemed to be for help wanted) has revived plans to throw a bridge and oil-access highway across the river upstream from the site, now technically known as the Elkhorn Ranch Unit of Theodore Roosevelt National Park.
But is also used metaphorically.
There, the trappings of period serve to throw a bridge of continuity between the classics of yesteryear and the present, rather in the way that the Grammys always go to modern versions of 50s soul acts: Amy Winehouse, Adele, Norah Jones.
If Kant has already established that on the basis of our awareness of our obligations under the moral law we can be confident that we have free will and that all of the laws of nature are at least consistent with our realization of the ends commanded by the moral law, what more needs to be done in order to throw a bridge between the theoretical cognition of nature and the laws of freedom?
When he wrote this song, he was struggling to throw a bridge across his own troubled water.
Quotes seen on LudwigGuru
Note that the phrase is usually accompanied with a preposition such as across or between.
I have been searching for usages going back into military history...here is one:
The Delhi Gazelte has learnt your honour for it because iwice I have written you to edition that it is in contemplation to throw a bridge of pontoons across ...
Allen's Indian Mail and Register of Intelligence for British ...
I knew I had seen it used with 'pontoon bridge' before....