Suave is Giving Away 100,000 Bottles of Shampoo Tomorrow, 5/13! May 12, 2010 This post may contain a link to an affiliate. See my disclosure policy for more information. Suave will be giving away 100,000 bottles of FREE shampoo starting tomorrow, 5/13! You can see it referenced on the Rachel Ray show and starting tomorrow, you will be able to sign up for one!