Preheat oven to 350 degrees F.
Place yogurt in a large bowl. Mix in the baking soda and set aside. (This will react and get quite puffy)
In another large bowl beat the sugar, eggs and oil. Add bran and vanilla. Set aside.
Stir flour, baking powder and salt together; alternate adding the flour mixture and the activated yogurt mixture to the sugar and eggs mixture.
Gently stir in the blueberries.
Line muffin tins with papers and fill 2/3 full.
Bake at 350 degrees F for 30-35 minutes. (If your oven is like mine, check at 25 minutes and rotate the muffin tin to prevent over browning on one side!)