If I'm wearing a white shirt I usually wear an undershirt (wife beater though I don't currently beat wives) just in case. I also use a hair dryer to speed drying. Never had an issue with staining or at least staining not coming out.
I wouldn't worry about applying a ton to feel the burn. Generally don't feel much of one throughout the day, but trust me even 10, 12 hours later when you hit the gym (or the water from the shower) the burn will be there in full force!