Preheat oven to 425 F. Line two baking sheets with parchment and lightly grease.
Bloom yeast by stirring it with the warm water and the dough sugar. Let stand until foamy, 5–10 minutes.
Combine flour and salt in a large bowl. Pour in the yeasted water and melted butter, then mix into a shaggy dough.
Knead on a lightly floured surface until smooth and elastic, 5–7 minutes. Cover and rest 10 minutes.
Divide dough into 4 pieces. Roll each into a 3/4-inch rope and cut into 1-inch bites.
Bring the bath water to a gentle boil. Slowly stir in baking soda; adjust heat to maintain a simmer.
Boil pretzel bites in batches for 30 seconds, stirring so they don’t stick. Drain well with a slotted spoon.
Arrange on prepared sheets, spacing slightly. Bake until deep golden, 10–12 minutes.
Stir the coating sugar and cinnamon together in a shallow bowl.
Toss warm bites with melted butter, then roll in cinnamon sugar to coat on all sides. Serve warm.