Semi Bluff

Alright this question needs to be pre-luded by a hand that happened in a home game SnG.
We play these two times weekly: $50 and 8 players.
So theres 4 players left in. UTG a Gus Hansen like strategist, yet not as effective with $80. On the Button is a supertight/passive player with $64. I'm in the SB for $2 with $206 (I play and almost Erick Lindgren and Daniel Negraneu sort of game...I see a lot of flops and mix it up after flop usually outplaying my opponent). And in the BB for $4 is a player who will call any pre-flop raise with anything, with $40 in chips . He also never raises, no matter the situation. Very easy to read as well, because he is very chatty and stops talking when he has a hand worth playing.
UTG and the button fold to me, I raise it to $10 with A4s. He calls with
36os. Flop: 4 5 J rainbow. I lead out for $15 knowing that I'll likely take the pot down there(every pot that he and I are heads-up, I lead out for 3/4 pot). H then makes perhaps the worst play I've seen in awhile, he calls of 50% of his stack with a straight draw. Immediately I put him on a straight draw and plan on pushing in another $15 if a card higher than an 8 hits. When a K comes off on the turn I finished the bet and watch as he folds as expected.

I go on to win the Sng and $300. Now here's the question: If you were in the BB's situation, how would you have played that hand?

I personally would have pushed all in against a player like me who likes to bluff frequently. And even if I do call his push, he stil has a decent chance of making his hand.

I would foled 36o in BB to that raise.

So what if he pushed on the semi bluff? You would have still called getting 2-1 on the call with a pair, gutshot str8 draw and overcard. He was doomed.

His error was getting involved in the first place with garbage.

Guess he didn't realize that the flop call committed him to the pot.