Pre-heat oven to 400 degrees. Heat a non-stick pan over med-high/high heat, next add enough olive oil to coat the pan lightly. Season fish with salt and pepper and place the fish flesh side down. Saute for 3 - 4 minutes depending on how hot your pan/how thick the fish is. A good rule of thumb for fish of this style is 10 minutes for 1 inch thickness for it be considered cooked through. While fish is browning in pan check for color, a nice browned color is what you are looking to achieve. Flip filets over once, now skin side down and place in oven for about 8-10 minutes. If you want to check for doneness, use the sharp end of a steak knife, insert into the thickest part of the fish, and then lightly touch it with your lip. If it is hot, that is a good sign your fish is done. This striped bass is enjoyed somwhere around medium to medium well.
Other Notes
Wines that I think would be paired nicely - Old World White, preferably White Burgandy. Terre di Tuffi, a wonderful full bodied white wine originating from Tuscany. Those that prefer red, such as myself, could choose a light red, possibly a Pinot Noir from Sonoma or Montery. An alternative to pinot would be a lovely rosso di montalcino. The fish has depth of flavor, so an interesting wine is imperative