Wynn 8/16 hand what is better line?

[KHALI]

Playing at a decent 8/16 at the Wynn LV. By decent I mean most players are better than myself and are fairly tight and aggressive.

I am UTG+1 and am dealt Js Jh.

Hero raises and is called by loose player on the button. Have seen her call three cold with 86 off and seems to love any suited cards, to give you an idea of player. She also plays passive post flop and will call down with almost any piece. I have also recently beaten her out of two pots and she is a bit steamed at me.

Flop is As, 9s, 4h

I bet and villian calls.

Turn is Ks. Hero??? Is check and call line better here or is bet, call a raise and fold river unimproved line better?

If I didn't have Js I would lead and fold to a raise but having that Js which may or may not be redrawing to best flush made me question this one. Any thoughts?