Finely chop the onion so that it doesn't overpower the sauce.
Cook the chopped onion for 1 minute in the microwave to soften it.
Place the egg yolks in a saucepan and add the lemon juice. Stir until the mixture is well blended.
Add the first stick of butter, sliced into pats, and cook over very low heat stirring constantly until melted in.
Then add the next stick of butter in the same fashion continuing to stir constantly.
This process takes awhile because we want the egg and butter mixture to cook together.
If the heat is too high or you don't stir enough, the eggs will begin to cook on their own and the sauce will break. You'll know if/when this happens because you'll see lumps or curdles forming in your sauce.
If all goes according to plan, your sauce will begin to thicken and reach the point where it begins to look like a thin pudding. You'll see the line the spoon left after you drag it across the bottom.
Take the sauce off the heat, add the onions, tarragon and chervil and mix well.
Add the wine (if you don't have wine, you can substitute 2 tsp of lemon juice and 2 tbsp of water) and blend well.
Preheat oven to 350 degrees Fahrenheit and set a broiler pan to the side.
Cut the tenderloin into 1" cubes.
Take the bacon slices and cut each piece into thirds.
Wrap each filet bite in a piece of bacon and secure with a toothpick.
Heat a heavy skillet on high and sear each bite on all sides.
Transfer the seared pieces to a broiler pan and place in the oven for 15 minutes.
Serve filet bites with Bearnaise sauce.