How many bets? (there's no cap)

[Roy6]

Opponent is 33/4/0.74, over a large sample of hands. He pushes only strong hands and very strong draws (means he can't have an overpair on the turn).
He doesn't raise 99/44 here PF

Cryptologic 3.00/6.00 Hold'em <font color="#0000FF">(6 handed)</font> link

Preflop: Hero is SB with A[img]/images/graemlins/diamond.gif[/img], 5[img]/images/graemlins/spade.gif[/img].
<font color="#666666">2 folds</font>, Button calls, Hero completes, BB checks.

Flop: (3.00 SB) 5[img]/images/graemlins/heart.gif[/img], 5[img]/images/graemlins/club.gif[/img], 9[img]/images/graemlins/diamond.gif[/img] <font color="#0000FF">(3 players)</font>
<font color="#CC3333">Hero bets</font>, BB calls, Button folds.

Turn: (2.50 BB) 4[img]/images/graemlins/heart.gif[/img] <font color="#0000FF">(2 players)</font>
<font color="#CC3333">Hero bets</font>, <font color="#CC3333">BB raises</font>, <font color="#CC3333">Hero 3-bets</font>, <font color="#CC3333">BB 4-bets</font>,