If you don't want to crate train her - leash bond her to you. Keep her leash attached to you at all times. That way everytime she starts looking like she is going to go potty where she is not supposed to firmly say "no" and march her outside. When she does it in the area you want her too - praise greatly (don't forget the treats!!!)

And when I say keep the leash attached to you at all times - I mean even at night. That way if she moves away from you at night, it will wake you up and you can take her out. It will make for a few sleepless nights - but it will aid the housebreaking.