Strain the seeds from the passion fruit pulp with a fine-mesh strainer into a 2-quart saucepan. Add the sugar and water, then bring to a boil over medium-high heat, stirring until sugar dissolves.
Reduce heat to low and simmer until reduced to 1 cup of syrup, 10 to 15 minutes. Set aside to cool. Syrup can be made in advance and refrigerated for up to 1 week.
Fill a highball glass with 1 cup of the ice and set aside.
Combine 2 ounces of the passion fruit syrup, rum, lemon juice and remaining 2 cups of ice in a cocktail shaker. Cover and shake 5 to 6 times.
Strain into serving glass, add the bitters and enjoy. Paper umbrella or lemon twist optional.