We have several clients that clean both bouncy castles and marquees using a mixture of alkaline detergents and high pressure
Take care with regard to water discharge, depending where you are washing them, as wash water should not fall to a surface drain
When using detergents always start bottom to top, agitation will help
Rinse well, at least twice, top to bottom as any detrgent will dry and the water will evaporate leaving a 'sticky' residue that will be both an irritant to an infant and attract soiling again