How old is she? If she's around 8 to 12 weeks it could just be that she can't get to the litterbox fast enough. Kittens are just like kids and can get so involved in whatever they're doing that by the time they realize they need to go, they're too far away from the litter box, can't remember where it is etc.
Also, do any of the beds she's pee'd on have down comforters or a feather bed? I've got a cat who likes to pee on our down comforter if we don't keep our door shut. The best I can figure is she smells the feathers (prey animal) and scent marks them with urine as a form of either claiming the prey for herself or showing dominance.
You may also need more litterboxes than you currently have as some cats only like to pee in one and poop in the other. Or you're not cleaning the box enough/often enough for her.
Because of her age, I would just guess that she's not done with "potty training" and that confinement should help. This doesn't mean she has to spend days on end alone in a room. She can be out and about as long as there's someone to watch her. If they see her starting to squat or paw around like she's digging, they can swoop her up and plop her in the nearest litterbox. Remember to never punish her for peeing outside the box. She won't know why you're mad and it will just stress her out, potentially leading to more litterbox problems.
Also, if you want to make her an indoor/outdoor cat, please don't let her outside until after she's spayed (if she's not already). Female cats can become pregnant as soon as 4-6 months of age and they don't have to be in heat to get pregnant. They're induced ovulators, so the act of mating triggers the release of the eggs. Since she's still just a baby that's going to make it easier for a tom to catch her and mount her even if she's not in heat or receptive to him.
AAAAAAAND . . . Don't forget to clean all oops spots with an enzymatic cleaner (nature's miracle, simple solution) to get rid of all traces of the urine scent. Regular cleaners may make the smell go away to you, but she can probably still smell where she marked and she may go back to "refresh" the scent.