Your bet doesn't seem that bad, but a check is probably better. Two observations:

1) Your description seems to be of a fellow who is passive with his made hands but aggressive with his draws. Therefore, he very well could have a busted draw. The only thing we're worried about is him accidentally hitting the 6 on the river if he had some sort of crazy gutshot or a flush draw like yourself.
2) Your river bet is good if you think he'll fold out a pair of 5s or 9s. But if that's the case, why did he check his hand on the turn?

In conclusion, I'd say to check and win with ace high vs. his gutshot or flush draw. But it's a close decision. The big reason I might bet here is to disguise that you would raise the turn with a draw (from your prior descriptions of this game denying the passive players this information may be valuable enough to bet.)