Yes, bitters does have alcohol in it. Bitters is a concentrated blend of fruits, spices, herbs, barks and roots in an alcohol and water base. As of 2014, there are over 100 brands of bitters on the market, each with its own specific recipe and alcohol content.
One of the most well-known bitters brands, Angostura, which was created in 1824, contains approximately 44.7 percent alcohol by volume. Since bitters is commonly added to foods and beverages by the drop and is considered potable, it is classified as a non-alcoholic food ingredient. Many brands of bitters focus on a specific flavor element, such as orange, celery, fruit, aromatic spices or heat from capsaicin and black pepper. Bitters is a standard ingredient in classic cocktails such as the Manhattan and Old Fashioned.