If you need a shower cap but don't have one, look around the house for a substitute. This is a page about homemade shower cap ideas.
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Cut both handles on one side of a grocery bag. Invert bag and place on head, tucking hair under it. Draw the bag around your head and tie with what was once the handles up into a bow on top of head.
I have been using this idea for years as a "heat cap" when coloring my hair. Works great, and it's free!