Examine both the bust and the headstone. The base of the bust needs to be the same size or smaller than the marker. Also look at where the mounting pins are on the bottom of the bust. These pins determine where the holes are going to be drilled on the headstone. The mounting holes on the headstone need to be away from the edges, so the stone does not fracture.
Make a mark on the headstone where the pins from the bust rest. Drill the mounting holes in the headstone. The holes need to be a size or two larger than the pins on the bust. Mounting pins tend to be 3/8 inch in diameter, so a 5/8 inch hole is adequate. Drill deep enough so that the bust will set flush with the stone.
Fill the holes three-quarters of the way full of epoxy. Lower the bust onto the stone, with the pins going into the holes. If any epoxy is visible, wipe it away while it is still wet. The epoxy needs to dry and cure, then the project is finished.