What can I do to avoid my acne medication from bleaching my pillowcases and shirts?

I use a medication with Benzoyl Peroxide for my acne. It has bleached out my pillow cases and some of my t shirts. I’m going to stop using it because I’m getting new sheets. Does the medication have a half life should I be worried about it bleaching my new sheets if I haven’t used it for a day?
and will continue to not use it.
I dont have a major problem just about anything works, I need to know what wont bleach things.