Weigh the mirror on the bathroom scale and purchase J-hooks at the hardware store rated for the weight. You will need at least two and possibly three hooks.
Determine the center point of the mantel by measuring across it. Tape a quarter to a light string and place the quarter at that center point. Hold the other end of the string to the highest point of the wall above the mantel center point while standing on a ladder. Manipulate the string so that it pulls the quarter up slightly off the mantel. Let the quarter dangle freely and move the string left or right until the quarter is again directly over the center spot. Tape the top of the string to the wall near the ceiling and leave it. This is the center line on which you will place the center of the mirror.
Find the center of the mirror's width on the top edge with the measuring tape. Mark this spot with a thin line of masking tape.
Attach the hanging wire to the left and right back of the mirror with small screws. The screws should be approximately one-third of the distance from the top of the mirror, and lined up evenly. The wire should be taut between them. Place thin pieces of masking tape on the outside edges of the mirror showing where the screws are located.
Find the center point for the hanging wire. Measure the halfway point between the center point of the wire and the edge of the mirror for both sides. These are where the two hooks will hold the mirror to the wall.
Hold the mirror with one person on each side and, while standing on a ladder, place it to the wall so that the center of the mirror aligns with the center line shown by the hanging string and with the top of the mirror at the correct height. Place the bubble level on the top of the mirror and have the holders adjust their sides until the bubble is level. Place a thin piece of masking tape at the sides of the mirror equal to where the previously placed tape on the mirror shows the placement of the back screws. Remove the mirror.
Measure a distance left and right of the center line that is equal to where the hooks will hang the mirror, and level with the masking tape just placed on the wall. Mark these two spots with a small piece of masking tape. This is where the hooks go into the wall. Nail the J-hook into the wall on the left hand side of the center line. Place the edge of the bubble level on that J-hook and stretch it across to where the other hook will go. Ensure the bubble is level before mounting the other hook. If the bubble level is not long enough to reach to the other side then tape it to the center of a yardstick and use the yardstick to extend its length. If the mirror is exceptionally heavy, add a third J-hook directly in the center line and level with the left and right hook.
Remove the tape from all places except the piece at the top of the mirror showing the center line.
Place the mirror back against the wall and snag the wire to the J-hooks. Line up the center tape on the mirror top with the center line from the with string the quarter on it. Remove the tape from the mirror and remove the tape and line from the wall. The mirror is centered above the mantel and level.