Preheat the oven to 350ºF. Line a 13x9x2-inch baking pan with parchment paper, making sure there is enough overhang so the paper can be used as handles to lift the baked bars out of the pan.
In a large bowl whisk together the flours, brown sugar, oats, baking powder, salt, and baking soda. Using your hands or a pastry blender, rub the butter cubes into the flour mixture until the mixture resembles coarse crumbs. Transfer 1 1/2 cups of the mixture to a small bowl and reserve.
Add the egg white to the remaining flour mixture in the large bowl. Sir to combine. Add the blueberries and stir gently. Pat the crumb mixture into the prepared baking pan, using your fingers to press the mixture evenly over the bottom of the pan. Bake for 10 minutes.
Using an offset spatula, spread the blueberry preserves over the baked crust. Sprinkle the reserved flour-butter mixture evenly over the top of preserves. Bake for 30 to 35 minutes more or until golden brown.
Let the bars cool in the pan for 10 minutes. Using the parchment paper handles remove the bars from the pan and cool completely on a wire rack. Cut into bars.