Combine the warm water, yeast, and 1 tablespoon sugar. Let sit for 5 minutes until foamy. Stir in the flour, salt, and 2 tablespoons melted butter. Knead for 5 minutes until smooth and elastic. Cover and let rise for 20 minutes.
Roll the dough into long ropes about 1/2-inch thick, then cut into 1-inch pieces. Bring 4 cups of water to a boil in a large pot, add the baking soda, and boil the dough pieces in batches for 30 seconds. Remove with a slotted spoon and drain on a towel.
Preheat the air fryer to 375F. Arrange the boiled pretzel bites in a single layer and air fry for 8-10 minutes, shaking halfway through, until deep golden brown all over.
In a large bowl, mix the remaining 2 tablespoons melted butter over the hot pretzel bites. Combine 1/3 cup sugar and cinnamon in a separate bowl, then toss the buttered bites in the cinnamon sugar until coated.
Make the dip by beating together the cream cheese, powdered sugar, milk, and vanilla until smooth. Serve the warm pretzel bites with the cream cheese dip on the side.