In a 1-quart glass jar, combine all ingredients except the syrup. Cover and shake well. Let the mixture stand in a cool, dark place for two weeks, and shake the jar daily.
Strain the alcohol through a cheesecloth-lined funnel into a clean 1-quart glass jar. Squeeze any alcohol left from the cheesecloth into the jar and reserve the solids.
Repeat the straining process of the alcohol using a new cheesecloth into another clean jar to remove any sediments remaining. Cover the jar and set it aside for a week.
Transfer the solids retained after straining to a small saucepan. Add one cup of water to it and bring it to a boil.
Cover the mixture and simmer over low heat for 10 minutes. Remove the mixture and let it cool completely.
Pour the mixture into a clean 1-quart glass jar. Cover and let it stand at room temperature for a week. Shake the jar once daily.
Prepare the sugar syrup by dissolving one cup of granulated sugar in one cup of water over moderate heat. Let it cool before using.
Strain the liquid once again through a cheesecloth-lined funnel set over a clean 1-quart glass jar. Discard the solids. Strain again to remove any remaining sediment, if necessary.
Add the infused alcohol and sugar syrup. Cover and let the mixture stand at room temperature for 3 days.
Pour the bitters through a cheesecloth-lined funnel or strainer. Transfer it to glass dasher bottles. Cover and keep in a cool, dark place.