Add chocolate to glass, and chill: Drizzle chocolate syrup inside a martini glass. Place in freezer or refrigerator to chill while preparing drink.
Combine ingredients for martini: Fill a martini shaker 2/3 full with ice. Add vodka, Irish cream liqueur, chocolate liqueur, and chocolate bitters (if using).
Shake cocktail: Place lid on shaker; shake until well combined and chilled, 1 to 2 minutes.
Strain, and garnish: Strain the cocktail into prepared glass. Garnish with chocolate shavings or espresso powder, if desired.