Is the screw straight ?
If the screw is straight but running out bend it near the bearing by giving it a gentle whack with a soft hammer NEAR THE BEARING. Make sure you support the the free end with a bag of sand or your hand, otherwise the inertia can create a bend elsewhere because of the twang that will occur. Don't leave the end free, and give it little taps.
MARK THE HIGH SPOT with a marking pen. Don't do it by eye.
I have straightened bent valves while still in a head with just the right hit.
DON'T OVER DO IT. SNEAK UP and keep using the clock to check runout.
If the screw is not dead straight you must straighten it first.
With it not mounted in the bearing mark the low spot of of the bend and where it is along the screw, then holding the end of the screw a gentle whack on a piece of pine can bend it using the inertia of the whole rod.
Get a few bits of steel about the same size and practice first until you are confident you will not over do it. Get some demos from your friendly blacksmith if you can find one. This works for parts of all sizes. Just getting it right is a bit of an art.
PRACTICE FIRST. DON'T START WITH YOUR PRECIOUS SCREW which was bent by the welding.
Super X3. 3600rpm. Sheridan 6"x24" Lathe + more. Three ways to fix things: The right way, the other way, and maybe your way, which is possibly a faster wrong way.