How to play a Straight

[Etob_Pride]

I was in a game the other day and had the high straight off the flop, but there were two hearts on the board, creating a flush draw. I bet the pot and got two callers. Nothing came on the turn, so I bet the pot again, they both called. On the river another heart came, making a flush. One of the players bet a small amount, the other folded, and I just called. It turned out he had a set. Should I have stayed consistent and re-raise and bet the pot or was I right in just calling the raise?