Preheat the oven to 400 degrees F (200 degrees C).

Stir white sugar, brown sugar, tapioca, and salt together in a large bowl. Add rhubarb and blueberries; toss to coat.

Divide pie dough in half and roll each half out into a 9-inch round. Place 1 round of dough in the bottom of a pie plate. Pile rhubarb-blueberry mixture on top of dough and top with remaining dough round. Trim excess dough from the top crust to leave a 1/2-inch border below the top rim of the pie plate. Tuck the top edges of the crust under the bottom crust and crimp border together. Place pie plate on a rimmed baking sheet.

Bake in the preheated oven for 20 minutes. Reduce oven temperature to 350 degrees F (175 degrees C) and continue baking until the crust is golden brown and the filling is bubbling, 25 to 30 minutes more. Cool for 2 hours.