What did she bring with her from her room when she slept in yours? I presume pjs/nightie, cuddly toy, pillow?
I wonder if whatever it is is living in the seams of her pjs or pillow etc & surviving the w/machine? Perhaps try soaking her night clothes to see?
I would get a washing up bowl (or even a large pan or bucket), fill with really hot water & a squirt each of baby oil (anything mineral oil based) & washing up liquid, then l'd just leave them to soak for at least 6 to 8 hours (or even overnight - the longer the better). Then wring out the pjs (over the w/up bowl) & chuck into w/machine. Arm yourself with a magnifying glass & spoon to go "fishing" in the w/up bowl!
I'd be looking for anything with legs or perhaps anything that could be an egg. You could have a plate/ice cream lid nearby to chuck anything you might find on to have a proper look at/take to be identified.
I would do this with her nightwear/underwear for the next week or so, just to be certain.
Also the heat from the tumble dryer will kill insects - so you could just chuck her duvet/pillows/cushions in the dryer for a while - no need to wash first even- but obviously keep a close eye that things don't get so hot that they burn. Might be an idea to check the fluff screen thing after to see if there's anything with legs there too!
Anything that isn't suitable for the tumble dryer(cuddly toys) could be bagged & put into the freezer for a week or two.
The black specks that you've found in her bed could be nothing, or could be poop from whatever is biting her. I would collect it & look at it through a magnifying glass to try to determine what it is.
I would spray the entire house with Indorex
www.petmeds.co.uk/p-3454-indorex-household-flea-spray.aspx
The active ingredient in Indorex is Permethrin, which a quick google says is also effective against bedbugs(but suspect that you might need professional help as well if you have b/bugs). Don't forget to leave open wardrobe doors/drawers/airing cupboards before spraying.
Also, after years & years of using Frontline on my dogs, this year I've changed to Advantage. Their blurb promises to kill 99% of fleas within 24/48 hours. A quick look on pet meds shows that they do a cat version as well - so might be worth trying.
www.petmeds.co.uk/nsearch2.aspx?keywords=advantage+flea+cat
Hands up - I confess to being OTT!