If you'll take and make a center that you can chuck up in a drill chuck in the tail stock, it will help center the bolt handle in the fixture. The center needs to be stepped with two diameters. One diameter is turned down to the same diameter as the thickness of the bolt handle immediately behind the bolt knob. The second diameter is the same as the width of the bolt handle immediately behind the bolt knob. Now make a U shaped piece similar to a tuning fork that has two points of contact about 2" from each point that can be held in a tool post. Set each point to make contact on the outside of the lathe chuck which would pretty well set these two points parallel to the lathe bed. Now move down to the bolt handle in the fixture touching the right side point against either of the two diameters on the center. Move in and out moving from one diameter to the other on the center as you adjust the bolt handle in the fixture to touch the left side of the U shaped piece at the same time that the right side is touching the corresponding diameter in the center. Once you get the bolt handle aligned where it needs to be replace the center with a center drill and drill a center in the end of the bolt handle. Replace the drill chuck with a live center and you're ready to start turning down the bolt handle knob to the diameter that you want to thread it. Once you have the bolt knob turned down it takes less time to thread it with a die than it does to single point thread it in the lathe. You can do it either way, just be careful when you thread in the lathe as you can break the turned down section off if the threading tool goes too far down the shank.
The center drill will probably not appear centered in the center of the bolt knob when aligned with this method. However, that doesn't mean that it's not aligned with the bolt handle. The key to turning down a bolt knob in the lathe is to get the center drilled in the correct location on the bolt knob. If you get down close ( a .1 or .2" larger) to the diameter that you are trying to hit which is .312" for a Badger Ordnance knob and it looks like it's not going to be located correctly on the bolt handle, you can correct it in a mill by holding the bolt body between v-blocks and using a boring head with the cutter turned to the inside to move the turned down shank over a little to align it better. If the lathe work is done correctly, there is no need to adjust anything in the mill.
Turning down a bolt knob is certainly easier in the lathe than in the mill, but does take a little to get the bolt knob centered in the jig.
This may be as clear as mud, but it's a lot easier than trying to eyeball the bolt handle into alignment.