You may be more familiar with 'Simple Syrup' as 'Rock Candy Syrup' or Bar Syrup'. It's just a mix of 2 cups of sugar and 1 cup water. To make it yourself, boil the water and pour the hot water into the sugar and stir until all the sugar is dissolved. You can store it in any plastic bottle to have ready for mixing your cocktails.
You can use an inexpensive champagne or any sparking wine for this since you are mixing the wine with sugar and bitters.