The phrase "one's stand mixer bowl" refers to the bowl that is used in a stand mixer, which is a kitchen appliance used for mixing ingredients. Full definition
In stand mixer bowl combine 2 cups of flour, salt, oil, and the yeast mixture. (sugaredwhisk.com)
Transfer to your clean stand mixer bowl fitted with the whip attachment and whip the egg whites and medium then gradual to high speed until you have stiff peaks. (girlinthelittleredkitchen.com)
Clean stand mixer bowl and add egg whites; replace paddle with whisk attachment. (piarecipes.com)