Combine 1/4 cup water and sugar in a small saucepan and bring to a simmer, stirring until sugar dissolves. Remove from heat, and let cool completely. Refrigerate until ready to serve, or up to 1 week. (You can also add apple cider and bitters now, if you prefer, and refrigerate for 3 days, pouring in Champagne right before you serve.)
Combine syrup with Champagne, apple cider, and bitters in a large pitcher. Thinly slice apple lengthwise on a mandoline and place 2 slices in each Champagne coupe. Fill with punch.