Well,
This is what I do for what its worth.Have not done this alot but it worked well when I did.
1. With the muzzle pointed up, Pour a bit of quality penetrating oil down the bore and let it sit for a couple minutes. Not alot, several drops is enough. Then turn the rifle muzzle down and pour a few more drops of oil from the breech end and let sit a couple minutes.
2. Take a quality coated cleaning rod. I always use Dewey rods. Fit the Tip of the rod with the female thread adapter. This is very important. Will explain later. Also choose a cleaning rod that is as large as possible for the bore you are trying to clear.
For instance, if you have a 30 cal bore, do not use a 22 cal cleaning rod. We want as large of a rod as possible because it will reduce rod flap in the bore and increase the stiffness of the rod because the bore will help prevent rod bending.
3. Coat the rod with oil just for added lubrication. With the muzzle up and the rifle secured in this position, slowly feed the cleaning rod into the muzzle and down to where the bullet is stuck. Allow the female thread adapter to center over the nose of the bullet. This will also center the rod in the bore and help prevent bore ware as well as apply even centered pressure on the bullet. Much like a seating stem in a seating die. If you do not use the female thread adapter, you WILL damage the inside of your bore as well as deform the bullet nose making it much more difficult to remove the bullet.
4. Take a medium weight bench mallet, Not heavy, and lightly tap the end of the rod. It may take several taps to get the bullet moving but once it does and gets into the lubricated section of bore it generally slides quite easly with only light taps on the cleaning rod.
The light taps will also help limit rod flexing and bending as well. Watch so that the rod does not contact the muzzle hard when it is struck with the mallet.
I have yet to have a bullet not back out using this method. Very thin jacketed varmint bullets will be the trickiest because they deform so easily. With these go very slow and tap lightly to prevent the bullet from deforming to much.
THis is my method, it has worked so far.
Kirby Allen(50)