You have to use a double pole breaker to get 240v. The big wide double breakers catch both incoming hot buss bars so you get 2 totally separate 120v lines that are 180 degrees out of phase with each other. The skinny space saver two in one breakers only catch one buss bar so you can only ever get 120v out of them. Thats why those tiny double breakers have seperate switches. The 240v breakers will have both levers permanently tied together.
You need to base you wire and breaker size on what the bed draws, not the amperage rating of the plug on the end of the cord. There has to be a tag or plate somewhere on the bed that tells the volts and amps it requires.