I just got old baked in yellow armpit stains off my fiance's by sticking it in a bucket of hot water with a bit of automatic dishwasher soap and a 1/3 bar of fel's naptha soap. I let it sit for a week and then washed it and it came out looking brand new!
It shouldn't bleach your shirt just soaking it in water with soap. Basically you need to give the soap time to eat up all the oils and such in the deoderant.