There was an outbreak of Bed Bugs when we were in New York a few years ago. We were on the 26th floor of our Hotel and one morning we woke up with big red bites. We were told on the desk it was mozzies, but when we went to a chemist he confirmed it was bed bugs. He went on to tell us he had seen hundreds of cases. He further told us that bed bugs not only are present in beds, they get into furniture, carpets and clothes and when someone packs their case in an infected room they may take the bugs with them in their suitcase so infecting the next place they open their case.
When we went back to the Hotel and complained they changed our room and offered to launder our night clothes and any other clothes for free.
We got a change of room to the 23rd floor, but we did see the Exterminators in full coverall suits, face masks etc., They closed off the room and sprayed everything, after that the room was closed for a couple of days.
I read in the local N.Y. paper that bed bugs where a terrible problem in N.Y. and very difficult to get rid of.
So, it's not just a case of burning a mattress.
However, the other thing we were told is, people rarely see bed bugs, they come out at night and hide during the day. So if you have not been bitten you may have some other insect infestation.