My husband uses bitters in cooking fairly often. It has some alcoholic content. Hmmm... just got up and checked, it definitely has an alcoholic content. But you rarely drink enough of bitters to think much about it. I believe the drink you're talking about is called a pink gin. You shake a few drops of bitters in the glass, roll it around the glass to coat the inside of the glass, toss any excess. Pour gin into the glass and it will get a pink-ish hue. Some put bitters in Manhattans and Bloody Marys. But my husband also uses them to season his French onion soup and other dishes.
I, too, learned that it was invented by someone who was trying to increase the appetites of people who weren't eating enough when on tropical assignments.