Mix sourdough starter, warm water, and flour in a bowl. Cover and let sit overnight; the mixture should look bubbly and "spongy" in the morning.
Add sugar, salt and additional flour. Mix well.
Knead on a floured surface for 10 minutes, adding additional flour as needed. The dough should be firm. Place dough in a greased bowl, cover, and let rise until double (sour dough takes longer to rise than traditional yeast breads).
After punching down, divide dough into 12 balls. Make a hole in the middle of each ball with your thumb, and shape into a bagel shape, with a 2" hole in the middle.
Meanwhile, bring 2 quarts of water to boil on your stove-top. Drop 2 or 3 bagels at a time into the water; boil for 30 seconds, flip bagels over, and boil for an additional 30 seconds. Drain with slotted spoon and place on baking sheet.
Brush tops with egg white and add additional toppings if desired (poppy seeds, dried onions, etc.).
Bake at 350 for 35 minutes, turning once for even browning. Bagels are done when they are golden and shiny.