Since you opened preflop, and have lead out on the flop and the turn, there is a possibility that you're opponent doesn't put you on flush, infact if he is a semi-decent player, he would think that you're 3 barreling, since the heart on the river didn't scare you.
I think, do what most people wouldn't expect, make a big bet (3/4th of the pot), and bet quickly, such that you're opponent thinks, that your decision to bet the river was preplanned.
If your opponent had a weak king, or straight draw you were not going to win any more money from anyways, as he would've checked back or folded to value bet. Best thing to do is make your opponent believe that you're bluffing
, by betting quickly and betting big!