Well really a big part of potty training is to not allow them to have accidents unnoticed. She really should not have any opportunities to go to the bathroom on the bed or rug because if she's not potty trained she really shouldn't be allowed to wonder the house unsupervised.
Do you or have you considered crate training?
I can tell you what we did when our dog was a puppy, which worked very well (but it does, of course, take some time). We crate trained him. When no one was supervising him he was in his crate. When he was out of his crate we kept our eyes on him at all times. Some people will even attach the dog's leash to their belt loop to make sure the dog doesn't stray to far away.
I took my dog outside for bathroom breaks a lot, and rewarded him with treats and praise when he went outside. If he started trying to go inside I would calmly tell him "no", pick him up and bring him outside. Once outside I'd let him finish going and then reward him for going outside.
The key I think is to catch them every time, or just about every time, they try to go inside. You don't have to yell or anything, just take them outside and show them the right place to go then reward them for going where they are suppose too.
That's what I did anyways. It took some time and a lot of patience but was well worth it. My dog is 3 years old now and it's been years since he's gone to the bathroom inside the house.
Remember to clean the area where she has accidents really well too. You can buy enzyme cleaners at most pet stores that work really well at eliminating pet odors. If she can still smell an area where she peed, even if you can't, it will encourage her to go in that same area again.