I put 3-4" of organic mulch, a little past the drip line but I use a 'rain' nozzle setting when watering in the summer so the mulch does not wash away. If you do not havea nozzle, you may be better off leaving the hose on the soil until it has watered the area with the proper amount of water. I assume your water will come out with sort-of kind-of little pressure this way and will not wash away the mulch.

You could set a border of bricks along the edge of the patio to contain the mulch. You could put a soaker hose down and mulch over it and the water release would be slow enough to not cause issues.