In a large bowl, dissolve yeast and sugar in warm water. Let sit until foamy, about 5-10 minutes.
Add flour, salt, and olive oil to the yeast mixture. Stir until a dough forms.
Turn dough onto a floured surface and knead until smooth and elastic, about 8-10 minutes.
Place dough in a lightly oiled bowl, cover, and let rise in a warm place until doubled in size, about 1 hour.
Preheat oven to 400°F (200°C).
In a mixing bowl, combine diced chicken, mayonnaise, ranch dressing, mozzarella, cheddar, bacon bits, and green onions until evenly mixed.
Punch down the dough and divide it into 6 equal portions.
Roll each portion into a circle about 6 inches in diameter.
Place a generous amount of filling in the center of each dough circle.
Fold the dough over the filling and seal the edges tightly to form a pocket.
Place pockets seam-side down on a baking sheet lined with parchment paper.
Bake for 20-25 minutes, or until the crust is golden brown with browned spots and the filling is hot and bubbly.
Serve warm, arranged on a white rectangular plate with a small ramekin of ranch dressing on the side.