Combine apricots, butter, nectar and honey in a small saucepan; place over high heat. Bring to boil, reduce heat and simmer 4 minutes or until apricots are plump. Remove from heat; cool.
Gently spoon flour into dry measuring cups; level with knife. Mix flour, bran, baking soda, and salt in a medium bowl, stir well. Add sugar mixture to flour mixture, stirring just until combined. Lightly fold in apricot mixture.
Spoon 1/2 cup batter into each of 7(6 ounce) ramekins coated with cooking spray. Place ramekins on a shallow baking sheet. Bake at 400*F. for 15 minutes or until golden brown. Put on wire rack.