First, shameless plug: Limit Hold 'em Heads-Up Poker Guide
There's a chapter there on playing overcards.
Having said that: Unless the board is very coordinated, you want to bet out. It's true that they won't always fold, but given the size of the pot (at least seven bets before you bet, meaning they're being offered 8:1 to call) it's enough that they fold sometimes
. What you're doing is essentially a semibluff with what might be the best hand. But you're hoping that they'll fold a bunch of outs.
On the turn, if both have called and you didn't improve, check. If the passive player called and you have ace-high (and the board didn't turn sour one way or the other) bet again. If he's loose/passive, he'll often call with many worse hands. Check the river. If he's passive and bets, you fold ace-high.
You say that you don't like knowing where you stand, but this is actually a mirage; you do know where you stand, or you should have some idea. If you know his preflop hand range, and you know that he'll call any flop, you should be able to figure out if you're ahead versus his range or not.
Edit: And I agree with AG in general, re: using the aggressive player as bait/tricking him into doing your dirty work for you. I'm aiming for how to play versus specifically the passive opponent.