In a large bowl, mix sourdough discard, warm water, yeast, honey (or sugar), and salt until combined.
Add bread flour and mix until a shaggy dough forms. Knead for 8 to 10 minutes until smooth, firm, and elastic.
Gently fold in blueberries, kneading lightly until evenly distributed without crushing them.
Place dough in a lightly greased bowl, cover, and let rise for 60 to 90 minutes until slightly puffy.
Punch down dough and divide into 8 equal pieces. Shape each into a ball, then poke a hole in the center and stretch gently into a bagel shape.
Place shaped bagels on parchment and let rest for 15 to 20 minutes.
Bring a large pot of water to a gentle boil and add baking soda. Boil bagels for 30 to 45 seconds per side, then remove with a slotted spoon.
Preheat oven to 425°F (220°C). Place bagels on a lined baking sheet and brush with egg wash if using.
Bake for 20 to 25 minutes until deep golden brown.
Cool on a rack for at least 20 minutes before slicing and serving.