Calling station question

[pufferfish]

You find yourself seeing the flop with 2 opponents, one of which is a "calling station".

The flop misses you entirely, but you do have one overcard (King).

Both opponents check to you.

Loose, non-calling station on your left will fold to a bet if he has nothing. Loose, calling station on your right will rarely fold. He will check/call all the way, and he bets as rarely as he folds.

Flop play: Do you bet to get it HU (with the calling station) and a "free" look at the turn?

Say you bet, next player folds, and calling station calls.

The turn misses you, and the calling station checks.

What's your play, check or bet?

Any comments would be appreciated.