Locate any wall studs that may be near the bulge with a stud finder. Make a note of these with an "X" mark so you don't accidentally cut into them. Draw a rectangle around the drywall bulge with a pencil and straightedge.
Use a drywall saw to cut out the rectangle. Measure the size of the rectangle and cut a new section of drywall to that size.
Cut out two 3-inch anchor blocks from a 2x4 for the new drywall square. Secure one anchor block into the corner of the wall you are repairing then mount a matching anchor block onto the back of the drywall. Use drywall screws to secure the new wall piece in place.
Use drywall screws and a drill to match up the anchor blocks embedded in the wall with the blocks on the reverse of the replacement drywall. Don't worry about any seaming issues that may arise during this step.
Flatten the seams on the new drywall square with mesh drywall tape. Spread drywall compound over the tape to erase the seam completely. Read the compound manufacturer's instructions for drying times since they can vary by brand. After the compound has dried, check it for smoothness. If it is still a little rough, add a second coat of compound. Do not sand the seams.