That's when it hit me: hadn't I just read about this situation on Parents Hacks?
Todd's secret for "no more tears" in the bath:
My daughter used to really hate getting her long hair washed and now she thinks it's somewhat fun. We used to use "tearless" shampoo but even that would sting her eyes if even a little bit of suds water got near them. What my wife and I came up with: we put a dry towel over our daughter's face and then dump a large plastic bowl full of shampoo and water on her head. We then rinse with fresh water in the same bowl until all of the suds are gone. No more fighting and it only takes a couple of minutes. Our daughter just turned 4 and for her it's fun feel a surprise of warm water hitting her head and body but not her face.
We do something similar (thanks to my mother in-law) -- my daughter holds a dry washcloth over her own eyes while we rinse her hair. Having a hand shower helps, too.
Without a moment to spare I ran to the linen closet while telling my wife to stop the rinse cycle. One dry hand towel over the eyes later and presto! No more tears. My wife and I almost couldn't believe how well it worked.
Parent Hacks - this stuff is gold, folks!