No one person invented the bed. They have evolved over time. From sacks filled with straw to cloth hand sewn and filled with horsehair as a mattress. In the orient they used and often still do use a simple straw mat to sleep on.
There is actually no definitive answer for who invented the bed. I'd like to think it was one of the Serta sheep because I love them. There have been different types of beds for millions of years. I want a Sleep By Number bed.