The phrase "across the bridge between" is correct and usable in written English.
It can be used metaphorically to describe a connection or transition between two different ideas, places, or states.
Example: "We need to find a way to communicate effectively across the bridge between our differing perspectives."
Alternatives: "linking the gap between" or "bridging the divide between".
In their smart camouflage gear and with AK47s slung around their necks, they swaggered up to the barrier across the bridge between the two countries.
His curly hair usually bounds up confidently when not pressed down by a bicycle helmet, but the bandage pulled it low and tight over swollen skin that cut diagonally across the bridge between his closed eyes.
Three wide rivers of footfall flooding across the bridge between the Aquatics Centre and the waterpolo arena and up to stand in the shadow of the stadium.
For over seven years I have went back and forth across the bridge between science and spirituality.
ACROSS THE BRIDGE: Stories, by Mavis Gallant.
The bridge between the two seems not to stretch all the way across the river.
Above the sparkling Tyne, 1,700 people stripped off at dusk and lay across the Millennium Bridge between Gateshead and Newcastle.
Bridge of Spies, by Giles Whittell, read by Jonathan Keeble (11½hrs unabridged, Isis, £30.49) In the early morning of 10 March 1962 two men walked in opposite directions across the Glienicke Bridge between West Berlin and Potsdam in East Germany.
From then on, he routinely walked across the Brooklyn Bridge between his office and his home in Park Slope, Brooklyn.
(It links Malmö in Sweden with Copenhagen in Denmark, and series one's first murder victim was laid across the bridge at the precise border between the two, a clever dual-jurisdiction conceit).
A group of old Chinese men, who sat in the park chatting and gazing across the river, said traffic across the formerly busy bridge between the two nations has diminished to occasional aid rather than thriving trade.
