Whats the plan
Where do you think you can fit a double bed if you have the rear bath and still want the sitting areas in the front...?
I did it opposite than your plan....I removed the double bed and replaced it in the far rear with a fold out couch/bed from an eighties model. A bed is wasted space, as far as I am concerned, for usable, daily space. So, I set up the rear sitting and living room as such. Then it is convertible to a bed only when I need it. The living area there has fold down table/desks, a wall mounted TV, speakers, appropriate lighting an ventilation.
"If it can't be reduced, reused, repaired, rebuilt, refurbished, refinished, resold, recycled or composted
then it should be restricted, redesigned or removed from production."