Yes, fleas. They will live in quite clean houses (and also in ours...).
The grubs crawl about in corners and in the carpet eating dust and debris -- this is why vacuuming helps. The grubs "crysalise", then hatch into adults, which keep quiet and wait until something warm passes by. Then they bite you!
One way of catching them is to sit on the bed with bare, sweaty feet on the floor (though you may not know anyone with those...?), and wait. They will come from quite a distance. Catch them by pinching smartly before they bite, then with a bit of juggling get them between your nails and crush them. Or drop them into a cup of soapy water -- they can't swim well. Hours of fun at bedtime...
A saucer of fresh blood is also supposed to attract them...