Can you setup an inflatable bouncy castle by yourself: yes you can.
You can easily setup bounce houses, smaller inflatables, and smaller slides by yourself. Typically it might take about 15-30 minutes to set up or take down a bounce house or a smaller inflatable.
Certainly experienced operators are also able to setup slightly heavier products themselves if they have the correct dolly or vehicle to help with transport.
However, it is advised for heavier units to have a second or possibly third person to help during the setup or the take-down process. Having a helper always makes the job faster. When setting up heavier inflatables that weigh several hundred pounds, it usually is necessary to have another person to help.