In Chuck Jones' Duck Amuck, Daffy Duck says: "What a way to run a railroad!" to complain about the absurdity of the situation. Daffy doesn't know this but he's talking to Bugs Bunny.
In John Ford's Mogambo, Kelly says to Victor (played by Clark Gable): "It's a fine way to run a railroad buster!", again to express absurdity.
Creators of Bugs Bunny (Chuck Jones & co.) were influenced by Clark Gable.
Both Duck Amuck and Mogambo were made in the same year, in 1953. I don't know which one was finished first.
I realize it was a common phrase at the time but still, it seems quite possible to me that Chuck Jones had seen Mogambo, which, according to Tag Gallagher's book on Ford, was a popular movie at the time ("Mogambo holds the record for first-year grosses of all Ford’s pictures."). And if my guess is correct, the fact that he stole a line of dialogue from the film hints that he probably enjoyed it too. At least, I'd like to think that way.