Usually, anything making heat is the largest consumer of watts around the house. Assuming that this will be running mostly at night, then more or less 100% of it is going to have to come from battery storage.
Realisticly though, you need to be powering more than just the bed. During power outages, you'll want to keep the lights on, and the refrigerator running? Let's assume you need ~3.0kWh of power just for 20th century necessities. Add on the consumption of the bed on top of that.
So, follow Darren's recommendation and add 3.0kWh to that. That will give you a ball-park number of what you will really need.