In this situation its important to get a read if you can. Otherwise i'd bet 2/3 pot regardless. You are gambling she does not have an A, if you are raiser PF and its HU its almost always EV+ to bet (unless board is like A-J-K or soemthign ridiculous and u know thy made soemthing.). If she dosnt have A, she will almost surely folded because there isnt much else she cna have hit with that flop. If she calls you are either up againt a pkt pair or A. If you get called, the turn will be very dificult for you, but i think the flop bet is in order.
on turn if you check and she checks beind u can bet your hand with confidence, if theres a reasonable bet than you are in a tough situation, it will cme down to your read.