If I was to use this method, I'd go with sewing thread or fishing line for the plumb line. It should make the alignment more precise.
I ran across this tool a while back. It mechanically levels your scope, without using a bubble level. It should work if the bottom of your scope's control cluster is square with your reticle and the flat on your scope mount/receiver is square with the plumb-plane through your bore axis.
http://arisakadefense.com/collection...-leveler-combo