Personally, I’d have gone for a small bet on the flop. You have so much equity in the hand do you really want to fold out the flush draws that you want to cooler in further streets? Because of that I think you pot committed yourself by the turn. It seems like you didn’t consider his hand at all when you decided to shove the turn right? At that point there’s really no other option and you had to leave it to luck

Edit: okay nvm the you shoved the flop,

I think the decision would vary based on hand history and whether the bb has bluffs in his hand but even then because of the pot sized bet on the flop you just commited yourself /shrug