Help me with theoretical thinking

[UtzChips]

I am 3 off the Button with J [img]/images/graemlins/club.gif[/img]T [img]/images/graemlins/club.gif[/img] and open/raise.
It's folded to the BB who calls with A [img]/images/graemlins/diamond.gif[/img]7 [img]/images/graemlins/club.gif[/img]

Flop: A [img]/images/graemlins/heart.gif[/img] 9 [img]/images/graemlins/club.gif[/img] 8 [img]/images/graemlins/diamond.gif[/img]

BB choses to go for the ck/raise.

I decide, that because:
1. I have OESD with BDFD, so I am going to bet it for value.
2. I open/raised and BB ck'd, I may be able to p/u the Pot right here.
3. If I can't p/u the Pot here, I may be able to get it on the Turn if a K falls and BB checks, which would be a pretty good indication he doesn't like the A/K on Board.
4. I open/raised PF, so my continuation bet on the Flop would be a rep of having an ace.

All decent reasons that I can think of for betting my hand on the Flop, when the BB checks. So I do.

The BB check/raises and I call.

My question: Am I paying 2 bets on the Flop to draw to my Straight, or am I paying only 1?

I would think I'm paying 1 bet to draw to my hand because the bet I made was for the reasons I've stated. Just because BB's ck/raise is a pretty good indicator that I am may very well be behind, I did not know that when I made my bet on the Flop, therefore, there was value in the bet that had nothing to do with my draw.

Is my logic wrong?