Prepare the area for the bullnose corner pieces. Install the baseboard trim as normal with each baseboard piece running up to the outside corner and terminating 1 inch from the edge of the rounded outside corner. Regardless of the size of the radius, stop the last piece of baseboard 1 inch back from the beginning of the radius on each side of the curve.
Cut the two sides for the bullnose piece. Measure scrap pieces of baseboard at 2 inches in length and cut them off straight with a chop saw. Set the angle of the chop saw to 22 1/2 degrees and cut the end off of one side of each of the 2-inch pieces.
Install the pieces adjacent to the straight baseboards running into the outside corner, with the straight cut against the other baseboard and the angle into the corner. Place them so the angles on the end of each piece angle inward toward the corner or outward toward the room, depending on how you look at it.
Fill the center gap between the two pieces to finish off the bullnose wrap. Measure the distance between the two angle pieces already installed on the wall and cut a small piece of baseboard scrap so that each side of the piece is at a 22 1/2 degree angle and slides into place between the two other sections.
Apply wood glue to the middle piece and slide it into the gap between the two outer pieces of the bullnose corner. Lock it in place with a wood clamp and use the same finish nailer you used to install the rest of the baseboard in your house to nail the middle piece into place. Wait 24 hours before removing the clamp.