Vacuum the sofa bed while it's closed with hose extension of your vacuum cleaner. Vacuum all surfaces, including crevices, thoroughly.
Open your sofa bed and remove the mattress and bedding. Wash the bedding in your washing machine with regular clothes detergent.
Repeat the vacuuming process with the opened bed, making sure to get to all of the crevices.
Take your mattress outside and use a broom to beat the dust out of it. This is the most effective method for getting dust out of your sofa bed mattress.
Clean up any spills or accidents with an organic, non-toxic cleanser. This type of cleanser is safe to use on the upholstery of your sofa bed.