I have done 3 barrels so far on my lathe. Some on here may cringe at how I supported the outboard side of the barrel, but sometimes you have to make due with what you have.
I bought a cheap roll of electrical tape, marked the barrel at the end of the outboard side of the bore, then started wrapping the tape around the barrel until it was a snug fit into the bore.
It actually got it within a few thousandths. Way better than not having any support. Plus, they all were 22lr barrels. 50-100 yards max, so I did not need the same amount of precision that a barrel for a 1000 yard centerfire match rifle would need.
I then indexed the it with the 4 jaw on the chamber end.
I shot one for the first time last weekend for the first time, and it shot great.