In a medium saucepan, combine the water, honey and sliced rhubarb. Bring to a simmer over medium heat, tilting the pan gently once in a while to dissolve the honey. When the mixture reaches a simmer, immediately turn off the heat, cover, and let steep for 30 minutes.

Gently strain the mixture into a heatproof bowl. Reserve the rhubarb for another use. Let cool to room temperature, then chill the syrup until cold. (If you're in a hurry, place the bowl in an ice bath and stir until cold.) The syrup will keep, refrigerated, for at least a week.

In a glass or measuring cup, mash the ginger with a muddling stick to break it up and extract the juice (a wooden spoon will work in place of a muddler). Add the syrup, gin, and lemon juice, stir well, then strain the mixture through a fine-mesh strainer into a cocktail shaker filled partway with ice, pressing on the ginger to extract all the good stuff. (A pint-sized mason jar with a lid works well in place of a cocktail shaker.) Add the bitters, if using. Shake the drink vigorously for 30 seconds, then strain into a smallish glass and enjoy.