For me, you did not play badly. It was just bad luck that the street was doubled on the river. I think I would have played similar to you.
If the BTN was a solid or conservative player, I would think that it has a premium combo in its hand (A-A, K-K, A-Ks)
If BTN was a very aggressive player, it could have double worse than yours.
But I could also have gotten a set on the flop (set of 2 for example, or 9 if it is a little less aggressive) but I assign this little chance.
So I think you did not play badly.
Greetings.