Your flop bet is fine. You bet 1/2 the pot, nice value bet to build the pot or semi-bluff to try and take it down if you don't hit.
Whenever you flop a flush draw, you have to always think like this:
There are 13 of a suit in the deck. 2 of them are in your hand, 2 are on the board. 13 - 4 = 9. So you have 9 outs.
To carry that farther, you can figure your hand odds
. You have 9 outs to make your flush. (I'm not going to count the 6 outs for hitting top pair here, just the flush because that more directly relates to your question).
On the flop you have 2 more streets to come. 9x4 (rough estimate of calculating hand odds) is 36. So you have a 36% chance of hitting your flush.
On the turn you only have 1 card to come so you take your outs (9) and multiple them by 2. Now your odds of making your flush just dropped to 18%.
BB bet about 1/2 the pot on turn. Calling is okay here. Reraising is also okay depending on your opponent. I'd probably just call if he is a calling station though, Only reraise if you think it will get him to fold.
You hit your flush on river so might as well reraise all in as you did to try and stack him.