No, chiggers will not spread and infest your bed or bedsheets. Unlike other parasites that can live and reproduce indoors, the chiggers a human would bring indoors are still in their larval phase and would likely brush off or be scrubbed off before making it to a host’s bed. Even if they did make it there, they would likely die before being able to reproduce. It’s still a good call to take a thorough shower after spending time outside.