"Bed mites" is a term that refers to two different organisms, bed bugs and dust mites. Both of these organisms can live in bedding, but they cause different problems and health issues.
Bed bugs live on a diet of blood. They hide in bedding during the day and come out at night to feed on humans. Bites leave visible rashes and cuts on the victim, and some people suffer from allergic reactions to the bites. It is possible that bed bugs carry disease. They are difficult to get rid of, and exterminating an infestation may require the destruction of all infested bedding.
Dust mites are often found in bedding and feed on dead skin flakes and hair. Most people can live with dust mites with no issues, but some have allergic reactions that may cause asthma, itching or hives. Washing bedding with hot water may decrease the number of dust mites, but they are generally difficult to get rid of.