No, it isn't, not unless it goes untreated for a really long time. Bedbugs live very nicely in squeaky-clean places, especially if those places are reliably climate-controlled. Give them the presence of humans and a constant 80F environment, and they couldn't be happier, even if the owners regularly break out the bleach.
DDT nearly wiped them out in the US, so much so that a lot of people didn't know that they were even real, but since DDT has been banned, they have made a comeback. There's a down side to restricting those toxic bug killers.
Bedbugs are fast, and they are mobile. They travel in on people's luggage and immediately go to ground in dark places. Unless the housekeepers are working in the dark and flipping the mattresses, they are probably not going to notice them. Changing the sheets every day helps to hide them, too -- if your sheets stayed on for a day or two more you would see the blood spots from the bites, but with clean sheets you don't notice as easily.
Leaving your luggage in a very hot car for several hours helps to keep them under control; they cannot take extreme heat. (Now that they can't use DDT, some hotels are sealing up rooms and baking the bugs with portable heaters.) If you can get the temperature up over 120F for several hours, they will all be deader than doorknobs.
They also tend to react badly to diatomaceous earth. You can use a brush to put some food-grade DE in all of the crevices of your bedroom furniture to help keep them from gaining a foothood in case you ever inadvertently bring them home from a trip.
PS: Removing the bedspread is totally useless in terms of warding off bedbugs. They don't live in the top bedding, they live in the MATTRESS. The closer to it you are, the more quickly they will be able to get to you. You would be better off sleeping on top of that bedspread if bedbugs are what you're worried about.