Preheat oven to 350°F. Grease and flour a 9×5-inch loaf pan.
In a large bowl, blend together melted butter, eggs, buttermilk, bananas, and vanilla extract.
In a separate bowl, whisk together flour, sugar, baking soda, baking powder, and salt.
Stir dry ingredients into buttermilk/banana mixture in 3 or 4 additions. Gently fold strawberries into batter.
Scrape batter into prepared loaf pan.
Bake 1 hour, or until a cake tester inserted in the center comes out clean.
Let bread rest in pan for 10 minutes. Tip out of pan and let cool on wire rack for 20 minutes before slicing.
Wrap bread tightly in plastic wrap. It will keep on countertop for a day, in refrigerator for a few days. Slices of the bread taste great plain or toasted, and spread with cream cheese.