Looking at the late '55 shop manual, the worm gear bearing race is part of the adjusting nut, it's the way the other years are also. https://www.flickr.com/photos/advance-design_parts_co/sets/72157632210242370/
Yours will be very similar to the one shown in the manual I linked. If the sector shaft only has one bushing on the long side, then the second bushing will need shortened to fit the cover, just be sure it's not needed on the long side first. When rebuilding my '41 box, I was buying bushings at my local bearing distributor since they were standard sized, I added a second bushing to the long side to give more support out on the seal end, it really tightened up the movement at the seal.