Bet the flop = Good
I would raise the turn with the outs and put BB on a smalll stright draw or pair of Q's at best.
You have 6.5 or 7 outs and about 7.5:1 implied pot odds.
BB may fold to your raise and you win (4 BB), or he calls and then you c/b the river. If you lose it's only one extra bet. So you are risking 1 bet for possible 8.