I use to use a wooden disc on the headstock with a Foam Pad between the Bowl and the Disc, then bring up the Tailstock fitted with a suitable Rvolving Centre.
Check for concentricity [It is a good idea when turninmg the Tenon to make a small indent, using the tip of a Skew, to mark the centre] and then carefully modify or turn away the Tenon with just a small spigot left where the Centre is.
Remove from Lathe and using a Sharp Chisel remove this spigot and sand to a finish.
However these days I tend to use my Vacuum Chuck whenever possible for this.
Richard