The problem here is the English sentence, not the Klingon. One doesn't say cross under a bridge to mean travel along a path that leads under a bridge. One might say go under a bridge or travel under a bridge, but not cross under a bridge. At least, not that I've ever heard.
The Klingon sentence, on the other hand, means exactly what it says: we cross the area that is under the bridge.
Cross under the bridge is in use in English. One of the examples below is from my own city. It may however be telling that the first definitively American result (the Colorado bridge one could be a foreign tourist) is from 1893. If it's truly not valid in modern American English, you're right: it should probably be changed, given that the Duolingo flag for English is the American one. It's often very surprising to me which words and expressions are not used by our southern neighbours. I got a lot of blank looks trying to find the parkade where we'd left the rental car in San Francisco. I thought it was just that we were asking people who didn't drive, thus didn't pay any attention to the location of multi-storey parking lots.