Does Medicare cover a hospital bed if ordered by a doctor?

Yes. Both my parents needed hospital beds. It's by rental in which Medicare will send monthly the rental $$. You will need to make sure that the Home Care supplier accepts Medicare. Also, since mom was bedridden for over 13 years, eventually years later, Medicare sent a letter to mom with the option to Own the hospital bed. Which my dad accepted.

Check this out..
http://www.medicare.gov/coverage/hospital-beds.html