Shake, Collins glass with cracked ice, top off with club soda, garnish with lime slice or shell of spent lime.
Homemade grapefruit syrup recipe: 1 cup sugar, 1 cup water, zest and juice of 1 grapefruit (discard the pith and pulp), optionally add a pinch of salt and a squeeze of lemon. Bring to a boil, then take off the stove and let steep 1 hour, strain through cheesecloth and bottle. Optionally add 2 tsp vodka as a preservative. Keep in refrigerator.
The Paloma is traditionally made with commercially-available grapefruit soda pop. This recipe replaces soda pop with homemade grapefruit syrup and dashes of bitters.
See http://www.homebarbasics.com/la-paloma/ for history and notes about the soda pop version of the Paloma.