Mix the bread flour, almond flour, instant yeast, sugar, and salt in a large bowl.
Blend the thawed blueberries into a puree, then work the puree and water into the dry ingredients to form a firm dough; add up to 2 more tablespoons of water only if dry flour remains.
Cover the dough loosely and let it rise in a slightly warm place for 60 to 90 minutes, until puffy.
Knead the risen dough by hand or with a stand mixer for about 3 minutes, until smooth, supple, and pulling away from the bowl.
Turn the dough onto a floured surface, shape it into a ball, and divide it into 4 equal pieces.
Mix the softened cream cheese and chocolate chips in a clean bowl.
Roll each dough piece into a thin 5-by-7-inch rectangle, add one-quarter of the filling, roll the dough over it, and pinch the long seam closed.
Join the ends of each filled roll to form a ring, pinch securely, place on a parchment-lined pan, cover loosely, and proof for 40 to 60 minutes until slightly puffy.
Heat the oven to 350°F and bring a pot of water to a gentle boil.
Boil each bagel for 30 seconds per side, then return it to the parchment-lined pan with a slotted spoon.
Bake for 20 to 25 minutes, until glossy and lightly browned, then cool completely before slicing or serving.