If you remove the bed, gently encase it in a plastic mattress cover before hauling it out. Disturbing any bugs in the mattress is bad. The objective is to get them out of your space.
Don't take ANYTHING from the camper into your house.
Diatomaceous earth works. Do some reading. In my personal experience, flea bombs aren't worth spit when it comes to BB. Don't waste your money, but, more importantly, don't waste time. They're multiplying as I type. Spray mixtures suggested previously might work. I couldn't say, one way or the other. My Cousin is a Building Engineer for Marriott, and he says they use heat in the offending room and all adjacent rooms, simultaneously. I never tried heat, but it sounds like the best/fastest way to be rid of them. A methodical, disciplined approach is highly recommended. Don't mess around. They are, truly, monsters in the night. It's all-out war until they're ALL gone. If it were me, I wouldn't go back in the house after being in the camper until I was in my Birthday suit, placing my clothes in a black, plastic bag and letting the bag sit in direct Sun for a few days (then, put them in the dryer). Or, simply throw the clothes away. It ain't worth the risk.