Mix butter, sugar, eggs and vanilla together. Mix flour, baking powder, and salt together. Reserve 1/2 cup of flour. Add the remaining flour to the sugar/egg mixture. Stir till mixed. Add the remaining 1/2 cup flour and the blueberries. You want the flour to coat the blueberries so they will not get too mushy.
Be sure to grease the Bundt cake pan very well with shortening and coat with flour so that it will come out of the pan easily. Bake at 325°F for 1 hour and 10 minutes in a Bundt pan. According to your oven you may have to cook the cake about five minutes longer. Let it sit about 15-20 minutes before you take it out of the pan.