Does such a thing exist? Right now I'm going through a bedbug scare.

Nope.  You can have bed bugs anywhere in a room (behind pictures hanging on the wall or in popcorn ceilings) because the attractant is not the bed itself but the warm blooded person that lays in it quietly for hours at a time.  Doesn't matter what kind of mattress you have.

^^ Truth. 

I guess I could kill myself. Take that bedbugs!

 

Perhaps a 1.2 million Euro magnetically supported bed, assuming you  can just keep your clothing and bedding completely unexposed to the critters in the first place...

I don't think there are any bedbugs in outerspace yet, so you could move to the International Space Station.  Zero gravity might make picking a mattress easier as well.

Here is a good article: http://thisbebutablog.blogspot.com/search/label/bed%20bugs 

 

Basically vacume your mattress and everything around it. dust with diatomaceous earth. seal in a allergy mattress cover. set feet in cup of diamaceous earth. etc.

 

good luck.