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Bitters usually do contain an alcohol content, with some ranging as high as 45%. However, it would be pretty hard to get a buzz from bitters because they are usually used in such small amounts to flavor a drink.
That being said, sugar alcohols are confusing. Sugar alcohols have nothing to do with the type of alcohol in beer, wine or spirits, and they aren't sugars either. A sugar alcohol, such as sorbitol or xylitol, is an incompletely absorbed carbohydrate. Since they are incompletely absorbed, you get only some of the calories, and your blood sugar goes up less than if you had had the same amount of sweetness with regular sugar. A rough but reasonable rule of thumb is to count about half the grams of sugar alcohol as sugar, for the purposes of counting sugar grams.