Hi,
Clark B's suggestion is right on.
Also when holding your barrel in the lathe chuck, three wooden wedges holding the barrel at the far side of the head stock will help keeping the barrel on center.
Cut the wedges ( hard wood ) about two inches ( 2" ) long.
Tap them in tight at 60 degrees intervals. Make sure the wedges are in the spindle hole the same distance.
This sounds much more complicated than it really is, but it really helps the barrel from wobbling in the chuck.
Afterwards rotate the chuck by hand with a dial indicator on the breech end "OR" just bring the tool bit holder, with a pointed tool bit in place as close as possible to a corner of the barrel.
If it is the same distance from the tool bit, you are ready to bore your breech.
NOTE: it is rather hard to turn a 30"+ barrel in a lathe and not have some degree of wobble, without support on the outside end of a lathe.
Generally for chambering, breeching, or threading of a barrel I have a special fixture with set screws at the outer left side of the spindle, that holds a barrel true.
Good luck on your venture!
Fred