The right chemical is permethrin. But it’s not actually very good at just killing bed bugs. It’s better used as a preventative measure. Great to use by spraying luggage and sleeping bags, clothing etc. before travel. It should be totally dry before you use whatever you’ve sprayed it on (it’s toxic when wet). Unfortunately, more and more bedbugs are becoming resistant to it.
The best way to get rid of bedbugs is heat followed closely by diatomaceous earth (which I can never pronounce properly). You can use a high-heat steam cleaner on your carpets, mattress, some clothing and some furniture. Then spread diatomaceous earth around the edges of your room, bed frame, closets etc - sparingly - you don’t really want to be breathing that stuff in large amounts. You can also clean out everything you own, take it apart and very carefully wipe it down with bleach.
Bed bugs are much more difficult to get rid of once they’ve infested your house, so if you think you might have picked them up while travelling, or sitting in a movie theatre, it’s best to get rid of them as soon as you can. Wash clothes and soft luggage in high heat washing machine and then dry on high heat for more than an hour. When in a hotel room keep luggage off the bed, preferably on a hard surface.
