Don't know what the situation is with the shaft.  But if you can get the shaft out of wherever its at, it's best welded up on a lathe. Chuck the shaft up, slow the lathe to a dead crawl and weld around and around the shaft.  Weld some,, let cool, weld some let cool weld some til the shaft is 'over built up' then turn down the shaft.

Welding up the shaft in the machine is more difficult. It can be cobbled up but not nearly as reliable or long lasting as using a lathe.

If there is room in the equipment and if the bearing sits in the middle of a long shaft, I would oversize the shaft when welding up and go to a bigger bearing and carrier.  I've no clue what the shaft situation is,  but a bigger bearing and carrier just gives some additional 'beef' where it never hurts to have more 'muscle'.