Fold pre-flop.

Flop: You just got called by the BB so he probably caught a peice of the flop and thinks you are full of dooty or has a big heart, which means the ace. Without reads it's tough to tell. The tighter the player the more I'm inclined to assume he has the flush and you are drawing thin.

Turn: I don't think a lead bet does anything for you here. If the BB raises what do you do? Give up the flush draw? Call when you could be drawing dead? Neither is very attractive and neither is check calling.

Folding pf would have saved you these ugly decisions.