What's that movie with the bridge and its builder?

You are certainly talking about David Lean's Bridge on the River Kwai from 1957.
Here's the IMDB plot description:

After settling his differences with a Japanese PoW camp commander, a British colonel co-operates to oversee his men's construction of a railway bridge for their captors - while oblivious to a plan by the Allies to destroy it.

Stars William Holden and Alec Guinness.

It's currently at #100 in IMDB's top 250 of all time. Definitely a classic.
Won 7 Oscars including Best Actor, Best Director, Best Picture, Best Screenplay (Pierre Boulle - better known for his Planet of the Apes novels, movies, and TV series).