As usual, no reads. How good/bad did I play this?

Turn, decide to fire with a good draw. River good scare card to fire?

PokerStars No-Limit Hold'em, $0.50 BB (6 handed) from (Format: Bet The Pot)

MP ($21.90)
Hero ($72.20)
Button ($26.55)
SB ($49.50)
BB ($48.50)
UTG ($55.20)

Preflop: Hero is CO with , .
2 folds, Hero raises to $2, 2 folds, BB calls $1.50.

Flop: ($4.25) , , (2 players)
BB checks, Hero bets $3, BB calls $3.

Turn: ($10.25) (2 players)
BB checks, Hero bets $6.5, BB raises to $13, Hero calls $6.50.

River: ($36.25) (2 players)
BB checks, Hero bets $25, BB raises to $30.5, Hero calls $5.50.

Final Pot: $97.25

I dunno, maybe because I've been playing at the $25 NL range and hardly ever go for a crazy bluff move myself I wouldn't play the turn or river like that. Since we know nothing about how the BB plays he could have anything here. He could've called with A3 PF for all we know. Or even something like T2 because he thinks it's cool to play the Brunson hand, who knows.

As played I'd probably check the river behind. After the turn CR there's a pretty good chance we need to improve. Unless he's only doing this with top pair, I don't see how the river serves as a usefull scare card uless he puts you on something like KK ot KT specifically I would think.

With a good draw on the turn against an unknown I really don't mind taking the free card because it would really suck to get raised off our hand here.

Wouldnt firing the turn be good to discourage floaters?
When I posted this, I thought he showed 34, but i realised it was 45